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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+64x^72+88x^74+227x^76+64x^77+188x^78+128x^79+62x^80+64x^81+50x^82+52x^84+24x^86+9x^88+2x^90+1x^148

The gray image is a linear code over GF(2) with n=312, k=10 and d=144.
This code was found by Heurico 1.16 in 0.406 seconds.