The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  X
 0  X  0  0  2 X+2  0 X+2 X+2  2  0  X  X
 0  0  X  0 X+2 X+2  2 X+2  2  0  X  2 X+2
 0  0  0  X  X  2  0 X+2  2  X X+2 X+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+62x^10+24x^11+145x^12+80x^13+108x^14+24x^15+53x^16+14x^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 0.0273 seconds.