The generator matrix

 1  0  0  1  1  1 3X+2  1 2X X+2  2  1
 0  1  0 2X+2  1 3X+3  1 3X  1  1  0  1
 0  0  1 3X+3  1  X X+1 3X+2  X 3X+3  1  1
 0  0  0 2X 2X  0  0 2X 2X 2X 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+212x^9+548x^10+1840x^11+3012x^12+1832x^13+520x^14+208x^15+11x^16+4x^17+4x^18

The gray image is a code over GF(2) with n=96, k=13 and d=36.
This code was found by Heurico 1.16 in 0.078 seconds.