The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X^2+1 X+1 X+1  0
 0  0  2  0  0  0  2  2  0  0  2  0  0
 0  0  0  2  0  0  2  0  0  2  2  0  0
 0  0  0  0  2  0  2  2  2  2  2  0  0
 0  0  0  0  0  2  2  0  2  0  2  0  0

generates a code of length 13 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+10x^8+24x^9+80x^10+320x^11+1060x^12+1104x^13+1064x^14+320x^15+77x^16+24x^17+8x^18+4x^20

The gray image is a code over GF(2) with n=104, k=12 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.