The generator matrix

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

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+53x^6+28x^7+280x^8+264x^9+1258x^10+996x^11+4542x^12+1520x^13+4564x^14+996x^15+1271x^16+264x^17+262x^18+28x^19+50x^20+7x^22

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 0.354 seconds.