The generator matrix

 1  0  1  1  1 X^2  1  1 X+2  1  1 X^2+X
 0  1  1 X^2 X+1  1 X+2 X^2+3  1  X X^2+X+1  1
 0  0  X X+2  2 X+2 X^2+X X^2+2 X^2+X+2 X^2  X  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+246x^10+384x^11+800x^12+384x^13+216x^14+15x^16+2x^18

The gray image is a code over GF(2) with n=96, k=11 and d=40.
This code was found by Heurico 1.16 in 1.61 seconds.