The generator matrix

 1  1  1  1  X  X  X  1  1  X  1  1  1
 0  X  0  X  0  X  X  0  0  2  X  X  X
 0  0  X  X  X  X  0  0 X+2  X  X  X  X
 0  0  0  2  0  0  0  0  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  0  0  0  2  0  2
 0  0  0  0  0  0  2  0  0  0  2  2  2
 0  0  0  0  0  0  0  2  0  2  2  2  0
 0  0  0  0  0  0  0  0  2  2  0  2  2

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+34x^6+139x^8+192x^9+580x^10+640x^11+1284x^12+2432x^13+1304x^14+640x^15+595x^16+192x^17+124x^18+28x^20+6x^22+1x^24

The gray image is a code over GF(2) with n=52, k=13 and d=12.
This code was found by Heurico 1.16 in 0.463 seconds.