The generator matrix

 1  1  1  1  0  0  2  1
 0  X  0  X  X  X  X  0
 0  0  X  X X^2+2  0 X^2  0
 0  0  0  2  0  2  2  0
 0  0  0  0  2  2  2  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+26x^4+140x^5+224x^6+692x^7+1930x^8+692x^9+224x^10+140x^11+26x^12+1x^16

The gray image is a code over GF(2) with n=64, k=12 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.