The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2+X  0
 0  0  2  2  2  0  0  2  2  2  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+19x^10+40x^11+135x^12+40x^13+20x^14+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.