The generator matrix

 1  0  0  0  0  1  1  1  1  0  2  X  1
 0  1  0  0  0  0  3 X+1  3  1  1  X X+2
 0  0  1  0  0  1 X+1  X  0 X+1  X  0  X
 0  0  0  1  0  1  X X+1  0 X+3  0  X  X
 0  0  0  0  1  1  0  2  1 X+3  X  X X+1
 0  0  0  0  0  X  X  X X+2  2  X  X  2

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+210x^7+859x^8+2884x^9+7923x^10+13694x^11+28025x^12+23800x^13+28171x^14+13614x^15+7944x^16+2948x^17+769x^18+194x^19+35x^20+1x^22

The gray image is a code over GF(2) with n=52, k=17 and d=14.
This code was found by Heurico 1.13 in 7.31 seconds.