The generator matrix

 1  0  1  1  1 X+2  1  1  1  1  0  2  X
 0  1 X+1 X+2  3  1  0 X+2 X+1  3  2  1  1
 0  0  2  2  0  2  2  0  0  2  2  2  2

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+84x^12+16x^14+27x^16

The gray image is a code over GF(2) with n=52, k=7 and d=24.
This code was found by Heurico 1.16 in 0.000775 seconds.