The generator matrix

 1  0  0  1  1  1  2  1  0  1  1  1  1
 0  1  0  1  X X+3  1  0  1 X+2 X+3 X+2  0
 0  0  1  1  1  0 X+1  X  X  X  X  0  0
 0  0  0  X  0 X+2  X X+2 X+2  X  0  2  2
 0  0  0  0  2  0  2  0  0  2  2  0  2
 0  0  0  0  0  2  0  0  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+72x^8+180x^9+306x^10+1140x^11+1154x^12+2472x^13+1166x^14+1160x^15+303x^16+164x^17+62x^18+4x^19+6x^20+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 1.16 in 0.203 seconds.