The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+28x^10+16x^11+68x^12+144x^13+228x^14+352x^15+381x^16+352x^17+228x^18+144x^19+52x^20+16x^21+28x^22+10x^24

The gray image is a code over GF(2) with n=64, k=11 and d=20.
This code was found by Heurico 1.16 in 26.1 seconds.