The generator matrix

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

generates a code of length 12 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+48x^9+395x^10+824x^11+1617x^12+758x^13+373x^14+60x^15+14x^16+6x^17

The gray image is a code over GF(2) with n=96, k=12 and d=36.
This code was found by Heurico 1.16 in 0.016 seconds.