The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+40x^9+96x^10+324x^11+294x^12+560x^13+280x^14+312x^15+87x^16+40x^17+8x^18+4x^19+2x^20

The gray image is a code over GF(2) with n=52, k=11 and d=18.
This code was found by Heurico 1.16 in 0.0157 seconds.