The generator matrix
1 1 1 1 1 1 1 1 X 1 X 1 1
0 X 0 X 0 0 X X+2 2 2 2 2 0
0 0 X X 0 X+2 X 2 X X X X 0
0 0 0 2 0 0 2 0 2 0 0 2 0
0 0 0 0 2 0 0 0 2 2 0 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+33x^8+24x^9+31x^10+128x^11+59x^12+464x^13+67x^14+128x^15+34x^16+24x^17+29x^18+1x^20+1x^22
The gray image is a code over GF(2) with n=52, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00538 seconds.