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 X^2  1  1  1  1  1  1  X  0 X^2+X  X X^2  1  1 X^2+X  X  1  0  1  X X^2  1  1  0  1  X  1  X X^2+X  1  0 X^2  1  1  X X^2+X  1  1 X^2  0  1 X^2+X X^2+X  1  X X^2  1  1 X^2+X  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  0 X^2  0 X+1 X^2 X^2+1 X^2+X  1  1 X^2+X X^2  X X^2+1  1  1 X+1  1  X  1 X^2  0 X^2+X+1 X^2+X  1 X^2  0  1  0  0  1  1 X^2 X^2+X+1  1  X X+1  1  1  0 X^2+X X^2+X  1 X^2+1  X  1  1  0 X^2 X+1  0 X^2+X+1 X+1  0 X+1 X+1  X
 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  1  X X+1 X^2+1 X^2+X+1 X^2+X+1  1  1 X^2 X+1  0  1 X^2+X+1 X^2+X X^2+1 X^2+X  0  0 X^2+X X^2+X+1  1 X+1 X+1  1 X+1  1  1  0 X^2+X X^2 X^2 X^2+1  0 X^2+X  0  1 X^2+X+1 X+1  1 X^2+X  0 X^2+X  X X^2+X+1  1 X^2+1 X^2+X+1 X+1  1 X+1  0  X X^2  0  X  X  0
 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  0 X^2 X+1  0  X X^2+1 X^2+X+1  X  X  1  1 X^2+1  X  0 X^2+X X+1 X^2+X+1 X+1 X^2+1 X^2  X X^2+X+1  X X^2 X^2+1 X^2+X+1 X+1 X^2+X  1 X^2+X X^2+X  1  0  X  X X^2+1  0 X^2+X X^2  1 X+1  1  0 X+1 X+1  0  1  X  1  X  1  1  X X^2+1 X+1 X^2 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  0  0  X X^2 X^2  X  X X^2  0  X  0 X^2  X  X X^2+X  0  0 X^2 X^2  X X^2+X X^2 X^2+X  X  0  0 X^2  X X^2 X^2+X X^2+X  0  X  X  0  0  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X X^2  X  X X^2 X^2  0 X^2  0  X X^2  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  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 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+154x^73+518x^74+766x^75+1210x^76+1396x^77+1874x^78+1890x^79+2319x^80+2350x^81+2812x^82+2314x^83+2820x^84+2354x^85+2532x^86+1970x^87+1653x^88+1276x^89+1006x^90+560x^91+413x^92+246x^93+204x^94+46x^95+25x^96+30x^97+12x^98+4x^99+5x^100+2x^102+2x^103+2x^104+2x^105

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 57.7 seconds.