The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^4+34x^5+57x^6+216x^7+1341x^8+236x^9+66x^10+24x^11+28x^12+2x^13+5x^14

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 0.016 seconds.