The generator matrix

 1  1  1  1  1  1  1  1  X  X  X
 0  X  0 X^2+X+2  2 X^2+X  0  X X^2+2  2 X^2
 0  0 X^2+2  0  2 X^2+2 X^2+2 X^2 X^2 X^2+2 X^2
 0  0  0 X^2+2 X^2+2 X^2 X^2+2  2 X^2  0 X^2+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+112x^8+128x^9+138x^10+1280x^11+164x^12+128x^13+84x^14+11x^16+2x^18

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 6.87e-008 seconds.