The generator matrix

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

generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+256x^71+1464x^72+3278x^73+6052x^74+9788x^75+15002x^76+20550x^77+26818x^78+30652x^79+33695x^80+30488x^81+28265x^82+21496x^83+14797x^84+8988x^85+5404x^86+2798x^87+1366x^88+590x^89+205x^90+106x^91+43x^92+18x^93+8x^94+6x^95+6x^97+2x^99+2x^105

The gray image is a linear code over GF(2) with n=640, k=18 and d=284.
This code was found by Heurico 1.16 in 706 seconds.