The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  1
 0  1  0  0 2X+2  1 3X+3  1 X+2 3X+2 3X 2X+2
 0  0  1  0 2X+3 X+1  X  1 2X X+2 3X+2 2X+2
 0  0  0  1  1  X X+1 X+1 3X+3 2X+3 3X+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+197x^8+1340x^9+4896x^10+14368x^11+23675x^12+14872x^13+4760x^14+1152x^15+254x^16+12x^17+8x^18+1x^20

The gray image is a code over GF(2) with n=96, k=16 and d=32.
This code was found by Heurico 1.16 in 3.66 seconds.