The generator matrix

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

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+60x^10+390x^12+60x^14+1x^24

The gray image is a code over GF(2) with n=96, k=9 and d=40.
This code was found by Heurico 1.16 in 3.81e-009 seconds.