The generator matrix

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

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+292x^73+1583x^74+3290x^75+6140x^76+10392x^77+15049x^78+20592x^79+26540x^80+30430x^81+33013x^82+30492x^83+27289x^84+21414x^85+15426x^86+9580x^87+5379x^88+2718x^89+1331x^90+656x^91+267x^92+154x^93+57x^94+22x^95+16x^96+8x^97+5x^98+2x^99+6x^103

The gray image is a linear code over GF(2) with n=656, k=18 and d=292.
This code was found by Heurico 1.16 in 738 seconds.