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

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+74x^47+175x^48+164x^49+321x^50+360x^51+526x^52+706x^53+922x^54+1164x^55+1339x^56+1630x^57+1544x^58+1586x^59+1383x^60+1196x^61+898x^62+762x^63+505x^64+344x^65+278x^66+132x^67+132x^68+50x^69+58x^70+16x^71+27x^72+6x^73+16x^74+2x^75+7x^76+5x^78+1x^80+1x^82

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 19.2 seconds.