The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+86x^57+382x^58+484x^59+1001x^60+1102x^61+1738x^62+1664x^63+2689x^64+2416x^65+3331x^66+2806x^67+3444x^68+2554x^69+2952x^70+1724x^71+1660x^72+906x^73+812x^74+372x^75+253x^76+150x^77+110x^78+52x^79+34x^80+16x^81+19x^82+2x^83+6x^84+2x^85

The gray image is a linear code over GF(2) with n=268, k=15 and d=114.
This code was found by Heurico 1.16 in 47.7 seconds.