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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+159x^54+16x^55+406x^56+256x^57+535x^58+208x^59+254x^60+32x^61+101x^62+57x^64+5x^66+17x^68+1x^100

The gray image is a linear code over GF(2) with n=464, k=11 and d=216.
This code was found by Heurico 1.16 in 0.235 seconds.