The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+185x^72+456x^73+826x^74+1078x^75+1380x^76+1784x^77+1964x^78+2330x^79+2608x^80+2608x^81+2623x^82+2666x^83+2456x^84+2272x^85+2047x^86+1678x^87+1309x^88+916x^89+644x^90+420x^91+226x^92+132x^93+76x^94+16x^95+23x^96+20x^97+9x^98+4x^99+2x^100+4x^101+1x^102+2x^104+2x^106

The gray image is a linear code over GF(2) with n=328, k=15 and d=144.
This code was found by Heurico 1.16 in 55.8 seconds.