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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+28x^50+62x^51+132x^52+192x^53+243x^54+260x^55+310x^56+310x^57+364x^58+444x^59+318x^60+334x^61+292x^62+212x^63+177x^64+120x^65+73x^66+62x^67+64x^68+32x^69+21x^70+16x^71+20x^72+2x^73+2x^74+2x^76+2x^77+1x^82

The gray image is a linear code over GF(2) with n=236, k=12 and d=100.
This code was found by Heurico 1.16 in 1.12 seconds.