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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+53x^46+54x^47+157x^48+220x^49+337x^50+354x^51+582x^52+698x^53+863x^54+1148x^55+1327x^56+1616x^57+1615x^58+1632x^59+1303x^60+1160x^61+849x^62+714x^63+569x^64+336x^65+304x^66+174x^67+120x^68+62x^69+65x^70+20x^71+32x^72+4x^73+7x^74+3x^76+2x^78+1x^80+1x^82+1x^88

The gray image is a linear code over GF(2) with n=232, k=14 and d=92.
This code was found by Heurico 1.16 in 17.7 seconds.