The generator matrix

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

generates a code of length 12 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+233x^8+1200x^9+4994x^10+14576x^11+23389x^12+14864x^13+4892x^14+1104x^15+278x^16+2x^18+3x^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 3.56 seconds.