The generator matrix

 1  1  1  1  1  1  1  1  X X^2  X  1
 0 X^2+2  0 X^2+2  2 X^2  2 X^2 X^2+2 X^2+2  0  0
 0  0  2  2  2  2  0  0  0  2  0  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+6x^10+34x^11+39x^12+44x^13+1x^14+2x^15+1x^18

The gray image is a code over GF(2) with n=96, k=7 and d=40.
This code was found by Heurico 1.16 in -1.01e-007 seconds.