The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+98x^44+26x^46+346x^48+250x^50+96x^51+878x^52+288x^53+1128x^54+608x^55+2272x^56+1056x^57+2324x^58+1056x^59+2284x^60+608x^61+1098x^62+288x^63+859x^64+96x^65+274x^66+296x^68+20x^70+104x^72+26x^76+2x^80+2x^84

The gray image is a linear code over GF(2) with n=232, k=14 and d=88.
This code was found by Heurico 1.16 in 18.5 seconds.