The generator matrix

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

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+182x^72+430x^73+818x^74+1108x^75+1541x^76+1558x^77+2147x^78+2130x^79+2642x^80+2536x^81+2853x^82+2470x^83+2676x^84+2160x^85+2109x^86+1550x^87+1404x^88+862x^89+671x^90+374x^91+257x^92+114x^93+66x^94+32x^95+31x^96+20x^97+2x^98+16x^99+2x^100+6x^102

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 56.1 seconds.