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

generates a code of length 68 over Z2[X]/(X^3) who�s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+137x^58+8x^59+357x^60+60x^61+584x^62+148x^63+759x^64+308x^65+870x^66+484x^67+913x^68+492x^69+794x^70+348x^71+690x^72+156x^73+509x^74+36x^75+270x^76+8x^77+138x^78+70x^80+34x^82+11x^84+4x^86+2x^90+1x^92

The gray image is a linear code over GF(2) with n=272, k=13 and d=116.
This code was found by Heurico 1.16 in 6.14 seconds.