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.