The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1  1  0  1 X^3+X  1  1  1  1  1 X^3  1  0 X^2+X  1  1 X^3+X^2+X  1 X^2  1 X^2+X  1  X  1  1  1  1 X^2  X  0  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1 X^2+1  0  1 X^3+X+1  1 X^3+X^2+X X^3+X^2+1 X^2  X X^2+X  1 X^2  1  1 X^2+X X^2+1  1  1  1 X+1  1  X X^3+X^2+X  0 X^3+X^2+X  0 X^2+X  0  X X^2 X^2  X
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3 X^3  0  0 X^2  0 X^3+X^2 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^2  0 X^3 X^2 X^2 X^3 X^2  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0  0  0 X^3  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+580x^54+944x^56+1184x^58+838x^60+436x^62+71x^64+24x^66+16x^70+2x^76

The gray image is a linear code over GF(2) with n=464, k=12 and d=216.
This code was found by Heurico 1.16 in 97.8 seconds.