The generator matrix

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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+408x^64+492x^65+1396x^66+1016x^67+2182x^68+1592x^69+2908x^70+2056x^71+3311x^72+2156x^73+3444x^74+2008x^75+3068x^76+1484x^77+2092x^78+928x^79+1067x^80+360x^81+428x^82+128x^83+134x^84+60x^85+32x^86+8x^87+5x^88+4x^90

The gray image is a linear code over GF(2) with n=292, k=15 and d=128.
This code was found by Heurico 1.13 in 17.7 seconds.