The generator matrix

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

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+56x^9+379x^10+816x^11+1649x^12+750x^13+357x^14+68x^15+14x^16+6x^17

The gray image is a code over GF(2) with n=96, k=12 and d=36.
This code was found by Heurico 1.16 in 0.031 seconds.