The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+131x^8+328x^10+192x^11+1060x^12+640x^13+1104x^14+192x^15+331x^16+104x^18+12x^20+1x^24

The gray image is a code over GF(2) with n=52, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0681 seconds.