The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 X 1 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X X X X 0 X X X X 0 X 2X X 2X 0 X 2X 0 0 2X 2X 2X 2X X X 0 0 X X X X X 2X 2X 0 0 X 0 0 X 2X X 2X 2X X 2X X X 2X X X X 2X 2X 2X X 0 2X 2X X 0 2X 0 0
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 0 X X X 0 X 2X X 0 0 X 2X 2X 0 0 X X 2X X X X X 0 2X 0 0 X 0 0 X 2X X X 0 X X 2X 2X X 0 2X X X 2X 2X X 2X 2X 0 X 0 0 0 2X X X 0 2X X X X 0
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 0 X 2X 0 0 0 X X 2X 0 X 0 2X 2X 0 X X 0 X X 0 X 0 0 2X X 0 X 2X X X 2X X X X 0 2X 0 2X 2X 2X X 2X X 0 2X 0 X 2X X 0 0 2X X 0 X 2X 0 0 0 0 2X 0
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X 0 2X X 2X 2X X X 0 2X X X X 0 X 0 0 0 0 X 0 X 2X 0 X 2X X X 2X 2X 0 X 0 0 0 2X 0 0 2X X 2X 0 0 X 0 2X X 2X X 0 X 2X 0 2X X 2X X 2X 2X X 0 0 0 X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 X 2X X 2X 2X 2X 2X X X X 2X 0 2X 0 2X 2X 0 0 X 0 0 X 0 0 0 X X 2X 0 0 0 X 2X X X 2X X 2X 0 X 2X 0 2X 0 2X X 0 2X 2X 0 2X 2X X 0 2X X 0 0 X X 2X X 2X
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X 2X 2X 0 X 2X 2X 0 0 X 0 X 2X 2X 0 2X 0 X 2X X X 2X 0 0 0 0 2X 2X X X 0 0 X 2X 2X X X 2X 0 2X 0 2X X 0 2X 2X 2X 0 0 X 0 0 2X 0 2X X X 2X 0 0 0 2X 2X X
generates a code of length 86 over Z3[X]/(X^2) who´s minimum homogenous weight is 153.
Homogenous weight enumerator: w(x)=1x^0+72x^153+172x^156+180x^159+234x^162+410x^165+940x^168+1626x^171+1606x^174+672x^177+126x^180+122x^183+94x^186+84x^189+88x^192+38x^195+36x^198+32x^201+12x^204+6x^207+8x^213+2x^243
The gray image is a linear code over GF(3) with n=258, k=8 and d=153.
This code was found by Heurico 1.16 in 1.86 seconds.