The generator matrix

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

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+53x^8+94x^9+217x^10+868x^11+1628x^12+864x^13+238x^14+92x^15+28x^16+2x^17+9x^18+2x^20

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.