The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 X X 1 X X 1 X X X X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 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 2X 2X 2X 0 2X 2X 0 2X 2X 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 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 0 2X 0 0 2X 0 0 0 2X 2X 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 2X 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 0 0 2X 2X 2X 2X 0 2X 0 0 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X 2X
0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 0 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 0
generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+45x^56+192x^57+15x^60+2x^72+1x^84
The gray image is a code over GF(2) with n=456, k=8 and d=224.
This code was found by Heurico 1.16 in 0.109 seconds.