The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  1
 0  1  0  0  1 X+1  1  2  X  1 X+2 X+2  3
 0  0  1 X+1  1  0  1  X X+2  2  2  3 X+1
 0  0  0  2  2  2  0  0  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+83x^10+112x^11+212x^12+242x^13+194x^14+78x^15+75x^16+14x^17+11x^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 1.16 in 0.00569 seconds.