The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+3x^12+20x^13+3x^14+4x^15+1x^18

The gray image is a code over GF(2) with n=52, k=5 and d=24.
This code was found by Heurico 1.16 in 0.00043 seconds.