The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1
0 2X 0 0 0 2X 0 0 2X 2X 0 0 2X
0 0 2X 0 0 2X 0 2X 2X 0 2X 2X 2X
0 0 0 2X 0 2X 2X 2X 0 0 2X 0 0
0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0
generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+7x^10+8x^12+224x^13+8x^14+7x^16+1x^26
The gray image is a code over GF(2) with n=104, k=8 and d=40.
This code was found by Heurico 1.16 in 3.81e-009 seconds.