The generator matrix

 1  1  1  1  X  1  1  0  X  1  1  X  1  1  X  1
 0  X  0 X+2  X  0 X+2  X  X  0 X+2 X+2  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  0
 0  0  0  0  0  0  0  0  0  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 8.

Homogenous weight enumerator: w(x)=1x^0+85x^8+76x^10+64x^11+296x^12+576x^13+320x^14+2432x^15+443x^16+2432x^17+440x^18+576x^19+184x^20+64x^21+160x^22+15x^24+28x^26

The gray image is a code over GF(2) with n=64, k=13 and d=16.
This code was found by Heurico 1.16 in 0.192 seconds.