The generator matrix

 1  0  1  1  1  0  X  1  1  X  1  1  1
 0  1  1  0 X+1  1  X  X X+2  2 X+1 X+1 X+1
 0  0  X X+2  0 X+2  X  X  0  X  0  0  0
 0  0  0  2  0  0  0  0  0  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  2
 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  0
 0  0  0  0  0  0  0  2  0  2  2  2  0
 0  0  0  0  0  0  0  0  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+34x^6+16x^7+171x^8+288x^9+1252x^10+1136x^11+3652x^12+3264x^13+3672x^14+1136x^15+1267x^16+288x^17+156x^18+16x^19+28x^20+6x^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 1.93 seconds.