The generator matrix

 1  1  1  1  1  1  X  1  1  X  X  2  0  X  2  1
 0  2  0  2  0  2  2  0  2  0  2  2  2  0  0  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+1x^16+12x^17+2x^18

The gray image is a code over GF(2) with n=64, k=4 and d=32.
This code was found by Heurico 1.16 in 0.000724 seconds.