The generator matrix
1 0 1 1 1 0 1 1 1 1 1 1 1
0 1 1 0 X+1 1 X 0 X+3 X+1 X+2 2 0
0 0 X X+2 0 X+2 X 0 X 2 0 X 0
0 0 0 2 0 0 2 0 0 0 2 2 0
0 0 0 0 2 0 2 2 2 0 2 2 0
0 0 0 0 0 2 2 2 2 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+35x^8+32x^9+119x^10+176x^11+487x^12+352x^13+485x^14+176x^15+116x^16+32x^17+33x^18+1x^20+3x^22
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 0.0129 seconds.