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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+36x^58+78x^59+139x^60+232x^61+242x^62+308x^63+401x^64+506x^65+573x^66+620x^67+685x^68+686x^69+703x^70+638x^71+538x^72+392x^73+358x^74+322x^75+230x^76+184x^77+88x^78+60x^79+42x^80+46x^81+41x^82+20x^83+9x^84+2x^85+7x^86+2x^87+2x^88+1x^92

The gray image is a linear code over GF(2) with n=276, k=13 and d=116.
This code was found by Heurico 1.16 in 6.05 seconds.