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 X X X X X X 2 X X X
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X+2 2X+2 2X+2 2 2X+2 2X+2 2X+2 2 0 0 0 2X 0 0 2X 2X 0 2X 2X+2 2 2 2X+2 2 2 0
0 0 2X 0 0 0 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0
0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 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 2X 2X 0 0 2X 2X 0 2X 2X 0 0
0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 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 2X 2X 0 0 2X 0 2X 0 2X
generates a code of length 57 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+48x^54+148x^56+128x^57+136x^58+40x^60+8x^62+1x^64+2x^80
The gray image is a code over GF(2) with n=456, k=9 and d=216.
This code was found by Heurico 1.16 in 0.156 seconds.