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  X  0  X  X  1  0  X X^2  1  1  1  0  X  1  1  0  X  1  X  0  X  1  1  1  1  1  X  1  X  X  0  1  1 X^2  1
 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  X X^2+X X^2  X  X X^2  0 X^2+X  X X^2  X X^2  X X^2+X  X X^2 X^2  X X^2+X  0  0 X^2+X  X  X  X X^2+X X^2+X X^2+X  0  X X^2 X^2 X^2  X X^2  X  X X^2+X  X X^2
 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  X X^2+X  0 X^2+X  0  X  X  X X^2  X X^2  0  X  X X^2  0  X  X X^2+X  X X^2  X X^2 X^2+X X^2+X  0  0 X^2 X^2 X^2+X X^2 X^2+X  X  X  0  X  0  X X^2+X X^2+X  X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0  0  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 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  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  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 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 X^2  0  0  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 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0
 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 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2
 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  0 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  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 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 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 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+221x^48+316x^50+68x^51+727x^52+356x^53+700x^54+944x^55+1050x^56+1680x^57+1032x^58+2072x^59+1185x^60+1720x^61+960x^62+944x^63+969x^64+336x^65+468x^66+68x^67+337x^68+4x^69+100x^70+90x^72+8x^74+23x^76+5x^80

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 19 seconds.