The generator matrix

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

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+98x^8+160x^9+1128x^10+1344x^11+1104x^12+160x^13+88x^14+13x^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.