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

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+120x^54+44x^55+238x^56+656x^57+172x^58+520x^59+96x^60+16x^61+64x^62+44x^63+48x^64+28x^66+1x^112

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 0.25 seconds.