The generator matrix

 1  0  0  0  1  1  1  X  1  1 X^3+X  1 X^2  1 X^2+X X^2 X^3+X^2+X X^3+X^2+X  0 X^3  1  1 X^2  1  1  1 X^2  1  1  1  1  1 X^3+X^2 X^3+X  1  1  1  0  1  1  1 X^3 X^3+X^2+X X^2 X^3+X^2+X  0  1  1  1 X^3+X^2+X  1  1 X^2 X^3+X X^2  1  1 X^2+X X^3 X^3+X^2+X  1 X^3+X^2+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1 X^2+X  0  1 X^2  1 X^3+X^2  1  1  1
 0  1  0  0  0 X^3+X^2+1 X^3+X+1  1 X^3+1 X+1 X^3 X^3+X  1 X^3+X^2  1 X^3+X^2  1 X^2+X  1 X^2 X^3+X X+1  1 X^3+1 X^2+1  0  1 X^2+X X+1 X^2+X X^3+X^2+X X^2+X  1  1 X^2 X^3+X^2+X+1 X^3+X  X X^3+1 X^3+X+1 X^3 X^3+X^2+X X^2  1  X  1 X^3+1 X^2+1 X^3+X^2  1 X^3+X+1 X^3+X^2 X^3+X^2 X^3+X  1 X^3+X^2+X  1  1  1  1 X^3+X^2+1 X^3+X^2 X^3+X  0  1 X^2+X+1 X^2+1  1 X^3 X^3+1  1 X^3+X^2  1  1 X^3+X^2+X+1  1  1  1  0 X^3+X+1 X^3
 0  0  1  0 X^2 X^3 X^3+X^2  0 X^3+1 X^3+X^2+X+1  1 X^3+1 X^2+1 X^2+1 X+1 X^3+X X^2+X  1 X+1  1 X^2 X^3+X X^3+X^2 X+1 X^3+X^2+1 X^3+X^2+X X+1  1  X X^3+X^2+X+1 X^3+X^2+1 X^3+X X^3+X^2+X X^2+1 X^3+X+1 X^3 X^3 X^3+X X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1  1  1  1  1 X^3 X+1 X^3+X^2+X X^3+X X^3+X^2+1 X^3+X^2+X  0  1  X  1 X^3+X X+1 X^2+X+1  1 X^2 X^3+1  X X^2+1 X^3+X X^2 X^2+1  X X^2+X X^2+X+1 X^3+X+1 X^2+1 X^3+1  0 X^3+X+1 X^3+1 X+1 X^3 X^3+X X^2+X X+1 X^3+X^2
 0  0  0  1 X^2+X+1 X^3+X^2+X+1 X^3  1 X^3 X^3+X^2+X+1 X^3+1 X^2 X^3+X^2+X+1 X^3+X+1 X^2  1 X^3+1 X^3+X^2+1  1  X  0  0 X^2+X X^3+X^2+X+1 X^2+X X^3+X+1 X^2+X  1 X^2+X+1 X^3+X X^3+X+1 X^2  X X^3  X X^2+X+1 X^3+1  1 X^2 X^3+X^2+X X^3+X X^3+X X^3+X^2+X+1 X^2+1 X^3 X^3+X X^2+1 X^3+X^2+X+1 X^3+X^2 X^2+X+1 X^3 X^3+X^2+X X^3+X^2+1  1  1 X^3+X^2+1 X+1 X^3+X X^2  X  0  1  X X^3+1 X^3+X^2+1 X^3+X  1  X  1 X^3+X X^2+X+1 X^2+1 X^3+X^2+1 X^2+X+1 X^3+1 X^2+1 X^2+1 X^3+X^2+X X^3+X X^3+1 X^3+X^2
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+332x^73+1634x^74+3148x^75+5693x^76+7652x^77+11050x^78+12740x^79+15721x^80+15472x^81+15787x^82+12992x^83+11276x^84+7166x^85+5120x^86+2648x^87+1452x^88+640x^89+291x^90+152x^91+54x^92+18x^93+4x^94+12x^95+8x^96+2x^98+4x^99+3x^100

The gray image is a linear code over GF(2) with n=648, k=17 and d=292.
This code was found by Heurico 1.16 in 192 seconds.