The generator matrix

 1  1  1  1  1  1  2  X  X  X  1
 0  X  0  X  2  0 X^2  X X+2 X^2+2 X+2
 0  0  X  X X^2 X^2+X  X  X  0 X+2  X
 0  0  0  2  2  2  0  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+37x^8+260x^9+376x^10+718x^11+378x^12+218x^13+40x^14+18x^15+2x^17

The gray image is a code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.