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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+66x^48+82x^49+158x^50+218x^51+276x^52+362x^53+434x^54+568x^55+692x^56+862x^57+857x^58+832x^59+720x^60+578x^61+426x^62+280x^63+221x^64+180x^65+136x^66+66x^67+68x^68+44x^69+36x^70+16x^71+4x^72+4x^73+4x^75+1x^90

The gray image is a linear code over GF(2) with n=232, k=13 and d=96.
This code was found by Heurico 1.16 in 4.58 seconds.