The generator matrix

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

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+48x^7+408x^8+1156x^9+3806x^10+7124x^11+13206x^12+14024x^13+13158x^14+7224x^15+3847x^16+1076x^17+378x^18+68x^19+10x^20+2x^22

The gray image is a code over GF(2) with n=52, k=16 and d=14.
This code was found by Heurico 1.13 in 2.22 seconds.