The generator matrix
1 0 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 3X
0 1 5X+1 3 5X+2 6 5X+4 X 4X+1 X+3 4X+2 X+6 4X+4 1 3X 6X+1 3X+3 6X+2 3X+6 6X+4 1
generates a code of length 21 over Z7[X]/(X^2) who´s minimum homogenous weight is 122.
Homogenous weight enumerator: w(x)=1x^0+882x^122+336x^126+1176x^129+6x^147
The gray image is a linear code over GF(7) with n=147, k=4 and d=122.
This code was found by Heurico 1.16 in 0.00147 seconds.