The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+52x^49+206x^50+426x^51+840x^52+1062x^53+1446x^54+2098x^55+2444x^56+2864x^57+3294x^58+3356x^59+3259x^60+3076x^61+2404x^62+1966x^63+1497x^64+956x^65+722x^66+378x^67+200x^68+102x^69+54x^70+30x^71+10x^72+16x^73+2x^74+5x^76+2x^79

The gray image is a linear code over GF(2) with n=236, k=15 and d=98.
This code was found by Heurico 1.16 in 40.4 seconds.