The generator matrix

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

generates a code of length 12 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+60x^9+218x^10+426x^11+666x^12+412x^13+182x^14+60x^15+21x^16+2x^19

The gray image is a code over GF(2) with n=96, k=11 and d=36.
This code was found by Heurico 1.16 in 0.015 seconds.