The generator matrix

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

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+31x^58+40x^59+77x^60+162x^61+263x^62+282x^63+312x^64+326x^65+356x^66+402x^67+370x^68+402x^69+297x^70+238x^71+228x^72+130x^73+58x^74+62x^75+26x^76+4x^77+12x^78+3x^80+2x^82+4x^84+3x^86+1x^90+3x^92+1x^94

The gray image is a linear code over GF(2) with n=268, k=12 and d=116.
This code was found by Heurico 1.16 in 1.05 seconds.