The generator matrix
1 0 1 1 1 X+2 1 1 0 1 1 0 1
0 1 X+1 X+2 1 1 0 X+1 1 0 X+1 1 0
0 0 2 0 0 0 0 0 2 0 2 2 0
0 0 0 2 0 0 0 0 2 2 0 2 0
0 0 0 0 2 0 0 2 2 0 0 2 0
0 0 0 0 0 2 0 2 2 0 2 0 0
0 0 0 0 0 0 2 2 0 2 2 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+26x^8+32x^9+125x^10+192x^11+616x^12+64x^13+616x^14+192x^15+125x^16+32x^17+26x^18+1x^26
The gray image is a code over GF(2) with n=52, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0102 seconds.