The generator matrix

 1  0  1  1  1 2X 3X+2  1  1 X+2  X  1
 0  1 X+1 X+2 2X+3  1  1 2X 3X+2  1  X 2X+1
 0  0 2X+2  2 2X 2X+2  0 2X+2  0  2  2 2X

generates a code of length 12 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+92x^10+272x^11+332x^12+224x^13+80x^14+16x^15+3x^16+4x^18

The gray image is a code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0.015 seconds.