The generator matrix

 1  0  0  0  1  1  1  X  X  1  1  2  1
 0  1  0  0  0  3  1  1  1  3 X+1  1  0
 0  0  1  0  1  1  X X+1  1 X+1  3 X+3  0
 0  0  0  1  1  X X+1  1  0  2  3 X+1  2
 0  0  0  0  2  0  2  0  2  2  0  0  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+36x^8+194x^9+380x^10+1090x^11+1372x^12+2020x^13+1394x^14+1140x^15+351x^16+154x^17+48x^18+10x^19+2x^22

The gray image is a code over GF(2) with n=52, k=13 and d=16.
This code was found by Heurico 1.13 in 0.212 seconds.