The generator matrix
1 0 1 1 1 3X+2 1 1 2 1 1 1
0 1 X+1 3X+2 2X+3 1 2 X+3 1 2X+3 X+1 X+1
0 0 2X 0 0 0 2X 2X 0 0 2X 0
0 0 0 2X 0 0 2X 0 0 2X 2X 0
0 0 0 0 2X 0 2X 2X 2X 2X 2X 0
0 0 0 0 0 2X 2X 0 2X 0 2X 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+28x^8+48x^9+222x^10+1168x^11+1164x^12+1168x^13+220x^14+48x^15+23x^16+6x^18
The gray image is a code over GF(2) with n=96, k=12 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.