The generator matrix
1 1 1 1 1 1 1 1 X X X 1
0 X 0 X+2 2X 3X+2 0 X 2 2 2 0
0 0 2 0 2X 2 2 2X+2 2X+2 2X+2 2 0
0 0 0 2 2 2X+2 2 2X 2X+2 2 0 0
generates a code of length 12 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+21x^8+126x^9+105x^10+124x^11+1284x^12+152x^13+102x^14+100x^15+20x^16+10x^17+1x^18+2x^20
The gray image is a code over GF(2) with n=96, k=11 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.