The generator matrix

 1  0  1  1  1 X^2+2  1  1  X  1  1
 0  1  1 X^2 X+3  1  X  0 X+2 X^2  0
 0  0  X  X X^2 X^2+X X+2 X^2+X+2 X^2+X X^2  2
 0  0  0  2  0  0  2  2  0  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+92x^8+336x^9+744x^10+1760x^11+740x^12+336x^13+72x^14+15x^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 0.016 seconds.