The generator matrix
1 1 1 1 1 1 X X X X 1 1 1
0 2 0 2 0 0 2 2 0 0 2 2 0
0 0 2 2 0 2 2 0 2 0 2 0 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+22x^13+3x^14+2x^17+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 0.000442 seconds.