The generator matrix

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

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+98x^10+80x^11+230x^12+224x^13+220x^14+80x^15+71x^16+18x^18+2x^20

The gray image is a code over GF(2) with n=52, k=10 and d=20.
This code was found by Heurico 1.16 in 6.98 seconds.