The generator matrix

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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+94x^63+189x^64+468x^65+431x^66+660x^67+643x^68+748x^69+619x^70+848x^71+571x^72+656x^73+504x^74+562x^75+354x^76+336x^77+178x^78+172x^79+55x^80+36x^81+18x^82+12x^83+9x^84+12x^85+9x^86+2x^87+2x^88+1x^90+2x^91

The gray image is a linear code over GF(2) with n=284, k=13 and d=126.
This code was found by Heurico 1.16 in 3.58 seconds.