The generator matrix

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

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+126x^16+1x^32

The gray image is a code over GF(2) with n=64, k=7 and d=32.
This code was found by Heurico 1.16 in 0.00139 seconds.