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 X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 X 1 X 1 X 1 X 1 1 1 2 X 1
0 2X 0 0 0 0 0 0 0 2X 2X 2X 0 2X 0 0 2X 0 2X 2X 0 0 0 0 0 2X 0 0 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 0 0 0
0 0 2X 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 0 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 0 0 2X 0 0 2X 2X 2X 0 2X 0 0 0 2X 2X
0 0 0 2X 0 0 0 0 2X 0 0 2X 0 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 0 0 0 2X 0 0 2X 2X 2X 2X 2X 0 0 2X 2X 2X 0 0 2X 2X
0 0 0 0 2X 0 0 0 2X 0 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 0 2X 0 0 2X 0 2X 2X 0 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0 0 2X 2X 2X 2X 2X 2X
0 0 0 0 0 0 2X 0 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 0 0 0 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 2X
0 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 0 2X 0 2X 2X 0 0 2X 0 0 2X 2X 2X 0 2X 0 0 0 2X 0 0 2X 0 2X 2X 2X 0 2X 0
generates a code of length 57 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.
Homogenous weight enumerator: w(x)=1x^0+39x^50+70x^52+83x^54+347x^56+1024x^57+330x^58+65x^60+38x^62+16x^64+11x^66+8x^68+7x^70+3x^72+4x^74+1x^76+1x^96
The gray image is a code over GF(2) with n=456, k=11 and d=200.
This code was found by Heurico 1.16 in 10.8 seconds.