The generator matrix

 1  0  0  1  1  1  0  X  X  2  2  1  1
 0  1  0  0  1  1  1  2 X+2  1  X  X  1
 0  0  1  1  X X+1  1  1  1 X+1  1  1  0
 0  0  0  2  0  2  2  0  0  0  2  0  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+77x^10+132x^11+216x^12+198x^13+202x^14+106x^15+71x^16+10x^17+9x^18+2x^19

The gray image is a code over GF(2) with n=52, k=10 and d=20.
This code was found by Heurico 1.11 in 0.0102 seconds.