The generator matrix
1 1 1 1 1 1 1 1 X X X X 1 1 1 1
0 2 0 2 0 0 2 2 0 2 2 0 0 0 2 2
0 0 2 2 0 2 2 0 2 2 0 0 0 2 2 0
generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+28x^16+2x^20+1x^24
The gray image is a code over GF(2) with n=64, k=5 and d=32.
This code was found by Heurico 1.16 in 0.000795 seconds.