The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X 1 1 X X X X 1 X X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1
0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 0 2X 0 2X 2X 0 0 0 0 0 2X 2X 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 0 2X 2X
0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0
0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 0 2X 0 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 0 0 0 2X 2X 0 0
0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 2X 0 2X 0 2X 2X 0 0 2X 2X 0 0 0
generates a code of length 70 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+15x^68+222x^70+15x^72+2x^86+1x^108
The gray image is a code over GF(2) with n=560, k=8 and d=272.
This code was found by Heurico 1.16 in 0.203 seconds.