The generator matrix

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

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+556x^54+832x^55+1242x^56+1232x^57+1168x^58+1112x^59+713x^60+408x^61+428x^62+200x^63+176x^64+56x^65+56x^66+11x^68+1x^72

The gray image is a linear code over GF(2) with n=464, k=13 and d=216.
This code was found by Heurico 1.16 in 669 seconds.