The generator matrix

 1  1  1  1  1  1  X  0  X  0  X  X  1
 0  X  0 X+2  0 X+2 X+2  X X+2  X X+2  0  0
 0  0  2  0  0  0  0  2  0  2  2  0  0
 0  0  0  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  2  0  2  2  0  2  0  0  0
 0  0  0  0  0  2  2  0  2  0  2  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+24x^8+2x^9+42x^10+50x^11+76x^12+108x^13+76x^14+76x^15+27x^16+18x^17+10x^18+2x^19

The gray image is a code over GF(2) with n=52, k=9 and d=16.
This code was found by Heurico 1.16 in 0.00207 seconds.