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 1 1 1 1 1 1 X X X X X X X X X X X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 X 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 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 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 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 0 2X 2X 2X 2X
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 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 0 0 0 2X 2X 0 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 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 0 2X 0 0 0 0
generates a code of length 86 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+11x^84+60x^85+144x^86+31x^88+4x^92+4x^101+1x^108
The gray image is a code over GF(2) with n=688, k=8 and d=336.
This code was found by Heurico 1.16 in 0.438 seconds.