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  X  1  1  1  1  1  1  1  1  1  1 X^2  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^2+X  0 X^3+X X^3+X^2 X^3+X  0 X^3+X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3 X^3+X X^2 X^2+X  0 X^3+X^2+X X^3+X^2 X^3+X X^3 X^2+X X^2  X  0 X^3 X^2+X X^3+X^2+X X^2  X X^2  X X^3+X^2 X^3+X^2 X^3+X X^3+X X^2+X X^3+X^2 X^3+X  X X^3+X  X X^3+X^2 X^2 X^2  0 X^2+X X^3+X^2 X^2 X^3+X
 0  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0  0  0  0  0  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  0  0  0  0 X^3

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+112x^53+9x^54+132x^55+128x^56+276x^57+751x^58+264x^59+124x^60+120x^61+7x^62+116x^63+2x^64+4x^65+1x^66+1x^112

The gray image is a linear code over GF(2) with n=464, k=11 and d=212.
This code was found by Heurico 1.16 in 0.281 seconds.