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.