The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+236x^74+292x^75+482x^76+304x^77+500x^78+308x^79+465x^80+204x^81+288x^82+152x^83+211x^84+112x^85+184x^86+76x^87+85x^88+48x^89+60x^90+28x^91+31x^92+12x^94+8x^95+5x^96+4x^97

The gray image is a linear code over GF(2) with n=320, k=12 and d=148.
This code was found by Heurico 1.11 in 0.453 seconds.