The generator matrix
1 1 1 1 X X X 1 1 X 1 1 1
0 X 0 X 0 X X 0 0 2 X X X
0 0 X X X X 0 0 X+2 X X X X
0 0 0 2 0 0 0 0 0 0 0 2 2
0 0 0 0 2 0 0 0 0 2 2 2 2
0 0 0 0 0 2 0 0 0 0 2 0 2
0 0 0 0 0 0 2 0 0 0 2 2 2
0 0 0 0 0 0 0 2 0 2 2 2 0
0 0 0 0 0 0 0 0 2 2 0 2 2
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+34x^6+139x^8+192x^9+580x^10+640x^11+1284x^12+2432x^13+1304x^14+640x^15+595x^16+192x^17+124x^18+28x^20+6x^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 0.463 seconds.