The generator matrix

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

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+121x^8+352x^10+192x^11+1066x^12+640x^13+1040x^14+192x^15+397x^16+80x^18+14x^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 0.0509 seconds.