The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+53x^4+32x^5+48x^6+160x^7+340x^8+320x^9+424x^10+1376x^11+3314x^12+4416x^13+2984x^14+1376x^15+721x^16+320x^17+120x^18+160x^19+169x^20+32x^21+8x^22+10x^24

The gray image is a code over GF(2) with n=52, k=14 and d=8.
This code was found by Heurico 1.16 in 0.175 seconds.