The generator matrix

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

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+92x^9+346x^10+906x^11+1434x^12+892x^13+310x^14+92x^15+21x^16+2x^19

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.