The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1
0 2 0 0 0 2 0 0 2 2 0 0 2
0 0 2 0 0 2 0 2 2 0 2 2 2
0 0 0 2 0 2 2 2 0 0 2 0 0
0 0 0 0 2 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 10.
Homogenous weight enumerator: w(x)=1x^0+7x^10+8x^12+96x^13+8x^14+7x^16+1x^26
The gray image is a code over GF(2) with n=52, k=7 and d=20.
This code was found by Heurico 1.16 in 0.000671 seconds.