The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  X  2 X+2  2
 0  0  X  0  0  0  X X+2  X  X  X  X  2
 0  0  0  X  0  X  X X+2  0  0  0  2  0
 0  0  0  0  X  X  0 X+2  X  0  2 X+2  0
 0  0  0  0  0  2  0  0  2  0  2  0  2
 0  0  0  0  0  0  2  0  2  2  0  2  2
 0  0  0  0  0  0  0  2  2  2  2  0  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+32x^6+96x^7+199x^8+380x^9+604x^10+944x^11+3248x^12+5356x^13+3276x^14+928x^15+615x^16+404x^17+180x^18+80x^19+32x^20+4x^21+4x^22+1x^24

The gray image is a code over GF(2) with n=52, k=14 and d=12.
This code was found by Heurico 1.16 in 0.454 seconds.