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  X  X  1  X  0  X  X  X  0  1  1 X^2  1  0  1  1  X  1
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0  X X^2 X^2+X X^2  X  X  X X^2  X  0  X X^2 X^2+X  X  0  0 X^2 X^2 X^2  X X^2  X  X X^2 X^2  0  0 X^2+X  X  X X^2 X^2+X X^2+X  0 X^2 X^2  X  X  X  X
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  0  X X^2+X X^2  0 X^2+X  X  X X^2+X X^2+X X^2  0 X^2+X  X  X X^2+X  0 X^2  X X^2+X  X  X X^2  X  X X^2  X  0 X^2 X^2+X X^2  X X^2  X X^2+X  0  0  0 X^2+X X^2
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X  X  0 X^2  0 X^2  X  X  X X^2  X  0  X X^2 X^2 X^2  X  X X^2+X X^2 X^2+X  0  0 X^2+X  X X^2  X X^2+X  0  X  0  0 X^2+X  X X^2 X^2+X  0  0
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X  X X^2+X X^2 X^2  X  0 X^2+X X^2 X^2+X X^2+X  0  X  X X^2+X  0 X^2  X  0  X  X  0 X^2  0 X^2 X^2+X X^2  X  X X^2  0  0  0 X^2+X X^2+X X^2  X  X
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2 X^2+X  X  0 X^2 X^2  0  X  0  X X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X  0 X^2+X  X X^2+X X^2+X  0 X^2  0  X  X  0 X^2+X X^2 X^2+X X^2+X  X  X
 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  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0 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 47.

Homogenous weight enumerator: w(x)=1x^0+68x^47+135x^48+214x^49+313x^50+358x^51+440x^52+556x^53+789x^54+1106x^55+1451x^56+1794x^57+1915x^58+1778x^59+1516x^60+1144x^61+794x^62+604x^63+435x^64+306x^65+228x^66+150x^67+103x^68+76x^69+52x^70+30x^71+14x^72+6x^73+4x^74+2x^75+1x^76+1x^94

The gray image is a linear code over GF(2) with n=232, k=14 and d=94.
This code was found by Heurico 1.16 in 17.5 seconds.