The generator matrix

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

generates a code of length 12 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+12x^10+32x^11+166x^12+32x^13+11x^14+1x^16+1x^22

The gray image is a code over GF(2) with n=96, k=8 and d=40.
This code was found by Heurico 1.16 in -3.24e-008 seconds.