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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+132x^54+127x^56+192x^57+290x^58+640x^59+224x^60+192x^61+158x^62+29x^64+46x^66+14x^70+2x^72+1x^104

The gray image is a linear code over GF(2) with n=472, k=11 and d=216.
This code was found by Heurico 1.16 in 37.8 seconds.