The generator matrix

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

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+28x^9+125x^10+282x^11+388x^12+416x^13+394x^14+260x^15+99x^16+36x^17+17x^18+2x^19

The gray image is a code over GF(2) with n=52, k=11 and d=18.
This code was found by Heurico 1.11 in 0.00777 seconds.