The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+212x^58+630x^59+947x^60+1518x^61+1551x^62+2140x^63+2187x^64+2834x^65+2799x^66+3274x^67+2753x^68+2780x^69+2299x^70+2290x^71+1558x^72+1258x^73+717x^74+452x^75+245x^76+172x^77+70x^78+42x^79+18x^80+12x^81+4x^83+3x^84+2x^85

The gray image is a linear code over GF(2) with n=268, k=15 and d=116.
This code was found by Heurico 1.13 in 14 seconds.