The generator matrix

 1  0  0  1  1  1 X^2+X  1  2 X^2+X+2 X^2+2  1
 0  1  0 X^2  1 X^2+X+1  1 X+2  1  1  0  1
 0  0  1 X^2+X+1  1  X X+1 X^2+X  X X^2+X+1  1  1
 0  0  0  2  2  0  0  2  2  2  2  0

generates a code of length 12 over Z4[X]/(X^3+2,2X) 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.