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.