The generator matrix
1 1 1 1 1 1 1 1 X 0 X X^2+2 1 1 X 2 1 X X^2 1 1 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 X^2+X X X+2 X 0 X^2+2 X^2+X+2 X 2 X X X^2 0 X^2+2
generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+8x^21+108x^22+8x^23+1x^24+1x^28+1x^36
The gray image is a code over GF(2) with n=176, k=7 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.