The generator matrix

 1  1  1  1  1  1  1  1  1  X  0  1  X
 0  X  0  X  0  2  X X+2  0  X  X X+2 X+2
 0  0  X  X  0  X  X  0  2 X+2  2 X+2  0
 0  0  0  2  0  0  0  2  2  0  2  0  2
 0  0  0  0  2  2  0  0  0  2  2  2  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+59x^10+32x^11+145x^12+64x^13+118x^14+32x^15+45x^16+15x^18+1x^20

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 0.047 seconds.