The generator matrix

 1  0  0  1  1  1  X  2  1  1  1  1  1
 0  1  0  1  X X+3  1  0 X+2 X+1  1  1  X
 0  0  1  1  1  0  1  1  3 X+3 X+1 X+1  1
 0  0  0  X  0 X+2  2  X X+2  X  2  0  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+56x^9+154x^10+270x^11+277x^12+512x^13+336x^14+252x^15+113x^16+56x^17+14x^18+6x^19+1x^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 0.017 seconds.