The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  2  0  0  2  2  0
 0  0  2  0  0  2  0  2  2  0  0
 0  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  2  2  2  0  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+9x^8+6x^10+224x^11+6x^12+9x^14+1x^22

The gray image is a code over GF(2) with n=88, k=8 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.