The generator matrix
1 1 1 1 1 1 1 1 X X X X 1
0 X 0 0 0 X X+2 X 2 0 0 2 0
0 0 X 0 X X X+2 0 0 X X 0 0
0 0 0 X X 0 X+2 X X X X X 0
0 0 0 0 2 0 0 0 0 2 2 0 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 2 0
0 0 0 0 0 0 0 2 2 2 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+37x^6+28x^7+167x^8+232x^9+348x^10+1252x^11+464x^12+3120x^13+478x^14+1252x^15+359x^16+232x^17+156x^18+28x^19+32x^20+5x^22+1x^24
The gray image is a code over GF(2) with n=52, k=13 and d=12.
This code was found by Heurico 1.16 in 0.118 seconds.