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

generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+435x^74+1440x^75+3211x^76+6490x^77+10096x^78+15732x^79+20832x^80+26564x^81+29307x^82+32678x^83+30393x^84+27856x^85+21057x^86+15600x^87+9465x^88+5468x^89+2979x^90+1392x^91+586x^92+310x^93+117x^94+74x^95+23x^96+12x^97+9x^98+6x^99+6x^103+1x^104+4x^105

The gray image is a linear code over GF(2) with n=664, k=18 and d=296.
This code was found by Heurico 1.16 in 768 seconds.