The generator matrix
1 0 1 1 1 0 1 1 1 1 0 0 X
0 1 1 0 1 1 0 X+1 0 X+3 1 1 2
0 0 X 0 0 0 X 0 X X 2 X X
0 0 0 X 0 0 X X 2 X+2 X+2 2 X
0 0 0 0 X X+2 2 X X+2 X X X X
0 0 0 0 0 2 0 0 0 0 2 2 2
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+121x^8+72x^9+528x^10+992x^11+1354x^12+1968x^13+1488x^14+992x^15+493x^16+72x^17+96x^18+14x^20+1x^24
The gray image is a code over GF(2) with n=52, k=13 and d=16.
This code was found by Heurico 1.16 in 0.244 seconds.