The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1  2 X^2+X+2
 0  1 X+1 X^2+X X^2+3  1  2 X+1 X^2+X+2 X^2+1  1  1
 0  0 X^2  0 X^2+2  0 X^2  2 X^2  2 X^2 X^2+2
 0  0  0  2  2  2  2  2  2  2  2  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+246x^10+384x^11+796x^12+384x^13+228x^14+3x^16+6x^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 0.266 seconds.