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  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
 0 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0
 0  0 X^3  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+19x^52+17x^54+27x^56+896x^57+27x^58+17x^60+19x^62+1x^114

The gray image is a linear code over GF(2) with n=456, k=10 and d=208.
This code was found by Heurico 1.16 in 0.125 seconds.