The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+8x^13+5x^14+1x^16+1x^18

The gray image is a code over GF(2) with n=52, k=4 and d=26.
This code was found by Heurico 1.16 in 0.0004 seconds.