The generator matrix
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 1 X X X X X X X 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 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 0 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 0 2X 0 0 2X 0 2X 0 0 2X 2X 0 2X 2X 2X 2X 2X 0 2X 0 0 0 0 0 0 2X 2X 0 0 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 2X 0 2X 0 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 0 2X 0 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X
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 0 2X 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
generates a code of length 56 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+6x^54+30x^55+201x^56+9x^58+6x^60+2x^71+1x^82
The gray image is a code over GF(2) with n=448, k=8 and d=216.
This code was found by Heurico 1.16 in 0.11 seconds.