The generator matrix

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

generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+72x^8+288x^9+888x^10+1600x^11+892x^12+288x^13+56x^14+11x^16

The gray image is a code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.031 seconds.