The generator matrix

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

generates a code of length 12 over Z4[X]/(X^2+2) 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 0.265 seconds.