The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  1
 0  1  0  1 X+2 X+3  1  0  3  1  0  0  0
 0  0  1  1 X+3 X+2  1 X+2 X+1 X+1  0  0  0
 0  0  0  2  0  0  0  0  0  2  0  2  0
 0  0  0  0  2  0  0  0  2  2  0  2  0
 0  0  0  0  0  2  0  0  2  2  0  0  0
 0  0  0  0  0  0  2  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  0  0  2  0

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+31x^6+64x^7+155x^8+320x^9+928x^10+1600x^11+2980x^12+4224x^13+2982x^14+1600x^15+931x^16+320x^17+152x^18+64x^19+28x^20+3x^22+1x^24

The gray image is a code over GF(2) with n=52, k=14 and d=12.
This code was found by Heurico 1.16 in 0.234 seconds.