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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+91x^48+152x^49+212x^50+244x^51+393x^52+530x^53+665x^54+846x^55+1098x^56+1420x^57+1674x^58+1796x^59+1630x^60+1468x^61+1090x^62+824x^63+650x^64+520x^65+358x^66+232x^67+201x^68+130x^69+85x^70+26x^71+32x^72+4x^73+11x^74+1x^90

The gray image is a linear code over GF(2) with n=236, k=14 and d=96.
This code was found by Heurico 1.16 in 18.1 seconds.