The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+40x^10+48x^11+121x^12+96x^13+117x^14+48x^15+37x^16+2x^18+1x^20+1x^22

The gray image is a code over GF(2) with n=52, k=9 and d=20.
This code was found by Heurico 1.16 in 0.00218 seconds.