The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 0 1 X^2+X 1 1 1 X^3+X^2 1 1 X^3+X 1 1 0 1 1 X^3+X 1 1 X^3+X^2 1 1 X^2+X 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X X X 1 1 1 1 1 X 1 X 1 1 0 1 X 1 X^3 1 1 0 1 X X^3+X^2 1 1 1 1 X^2+X 1 1 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X 1 X^3+1 X+1 0 1 X^2+X 1 X^2+1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3+X X^3+1 1 X^3+X^2 X^3+X^2+X+1 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 0 X^3 0 X^3+X^2 X^3+X^2+X X^3 X X^3+X^2 X^3 X^2+X X^2 X^3+X X X^3+X 0 X X X^3+X^2 X^2+X 1 X^3+X^2+X+1 X^3+X^2+X 1 X^3+X^2+X+1 X^3+X X^3+X^2+X X^2+1 1 X^2+X X^3+X^2+X X^2+X 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 X^3 X^3 0 0 X^3 0 generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+25x^74+224x^75+303x^76+384x^77+402x^78+516x^79+507x^80+436x^81+398x^82+424x^83+193x^84+136x^85+66x^86+52x^87+19x^88+4x^89+3x^90+2x^106+1x^128 The gray image is a linear code over GF(2) with n=640, k=12 and d=296. This code was found by Heurico 1.16 in 0.594 seconds.