The generator matrix
1 0 0 1 1 1 X+2 1 1 1 1 1
0 1 0 1 3X+2 3X+3 1 2 2 X 2X 2X
0 0 1 1 X+1 X X+1 X 3X+3 3X+1 0 2X
0 0 0 2 0 2X 2 2X+2 2 2X+2 2X+2 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+94x^8+286x^9+1152x^10+3422x^11+6476x^12+3440x^13+1132x^14+272x^15+101x^16+2x^17+4x^18+2x^19
The gray image is a code over GF(2) with n=96, k=14 and d=32.
This code was found by Heurico 1.16 in 0.266 seconds.