The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+190x^73+440x^74+902x^75+1044x^76+1514x^77+1586x^78+2334x^79+1876x^80+2728x^81+2352x^82+3056x^83+2203x^84+2982x^85+1830x^86+2206x^87+1619x^88+1538x^89+811x^90+632x^91+376x^92+218x^93+129x^94+76x^95+43x^96+40x^97+17x^98+10x^99+4x^100+6x^101+3x^102+1x^108+1x^112

The gray image is a linear code over GF(2) with n=332, k=15 and d=146.
This code was found by Heurico 1.16 in 58.6 seconds.