The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+96x^5+72x^6+288x^7+1098x^8+288x^9+72x^10+96x^11+18x^12+1x^16

The gray image is a code over GF(2) with n=64, k=11 and d=16.
This code was found by Heurico 1.16 in 1.05e-007 seconds.