The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+475x^72+1134x^74+1490x^76+1346x^78+1179x^80+935x^82+768x^84+507x^86+251x^88+73x^90+26x^92+3x^94+2x^96+2x^98

The gray image is a linear code over GF(2) with n=316, k=13 and d=144.
This code was found by Heurico 1.16 in 27.8 seconds.