The generator matrix

 1  1  1  1  X  X  X  1  1  0  1  1  X  X  1  1
 0  X  0  X  0  X  X  0  0  2  X X+2  X X+2  0  0
 0  0  X  X  X  X  0  0 X+2  X  X  0 X+2  0  0  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  2  2  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  2  2  2  0  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  0  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+71x^8+160x^10+32x^11+662x^12+416x^13+352x^14+1600x^15+1599x^16+1600x^17+352x^18+416x^19+676x^20+32x^21+160x^22+57x^24+6x^28

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 0.206 seconds.