The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0  1  1  1 X^2 X^2+X  1  1  1  X  X  1  X  1  1  1  0  1  1  1  0  1  1  1  1  0  1  1  X  1  1  1  1 X^2+X  1  1  1  X X^2  0  1 X^2+X  1  X  1  1  1  0  1  1  1  X X^2
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X X^2+1  1 X^2+X+1 X^2  1  0 X+1  1  1  1 X^2+X X^2+1 X^2+X  1  1 X+1  1 X^2+X  0 X^2+1  1  0 X^2+X X^2+X  1 X+1  X X^2+1 X^2+X  1  1 X^2+1  1 X^2+1 X^2 X^2+1  0  1 X^2+X X^2+X+1 X^2+X+1  X  1  1  X  1  0 X^2 X+1 X^2 X^2+X+1  1  1 X^2+X+1 X^2+X+1 X^2  X
 0  0  X  0 X^2+X  0 X^2+X  0 X^2+X  X X^2  X X^2+X X^2+X  0 X^2  0 X^2+X  X  0  0  0 X^2+X X^2+X  X  0 X^2 X^2  X X^2  0 X^2 X^2  X  X X^2+X  X X^2  0 X^2+X  X  X  X  0  X  X  X X^2 X^2+X X^2+X X^2+X  X X^2+X  X X^2+X  0  X X^2+X  X  0 X^2 X^2 X^2  0  X  X  X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  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 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 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+90x^58+76x^59+321x^60+156x^61+599x^62+432x^63+760x^64+544x^65+859x^66+616x^67+859x^68+632x^69+723x^70+368x^71+470x^72+192x^73+222x^74+44x^75+113x^76+12x^77+51x^78+31x^80+13x^82+3x^84+3x^86+2x^88

The gray image is a linear code over GF(2) with n=268, k=13 and d=116.
This code was found by Heurico 1.16 in 4.22 seconds.