The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1
 0  1  1 X+2 X+3  1  2  1  1 X+1  0  0  X
 0  0  X  0 X+2  2  X X+2  X  0  2 X+2  X
 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+28x^10+96x^11+69x^12+136x^13+68x^14+80x^15+17x^16+8x^17+8x^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 0.00235 seconds.