The generator matrix 1 0 0 1 1 1 X^3 0 X^3 X^2 1 1 1 1 1 X^3+X 1 1 X^2+X X^3+X^2+X X^2+X 1 X X 1 1 1 1 1 1 X^3+X^2 1 X^3+X^2 1 X^2 1 1 1 1 1 X^3+X X^3+X^2+X 1 0 1 X^2 1 0 1 X 1 X X^3+X 1 1 1 1 1 1 1 1 X^3 X^3+X 1 1 1 1 X^2+X 1 X 1 1 1 X^3 X^3+X 1 X^2+X 1 1 1 X^3+X^2+X 1 X^3+X 1 X X^2 X^2 X^3+X X^2 1 0 1 0 0 X^3+X^2+1 X^2+1 1 X^3+X^2+X 1 1 X^3 0 1 1 X^3+X X^2+X X X+1 1 1 X^3 X^3+X^2+X+1 1 1 X+1 X^3+X^2+X X^3+X^2+1 X^3+X^2+X X^2+X+1 X^3+X^2 X^3 X^2+X 1 X^3+1 1 X^3+X^2+X+1 X X^2 X^2+X+1 X^3+1 1 1 X^3+X 1 X+1 1 X^2+X 1 X^3+X^2+1 X X^3+X^2+X+1 1 1 X^2+X+1 X^2 X+1 X^3+1 X^3+X^2+1 X^3+X X^3+X+1 X^3+X 1 1 0 X^3+X^2 X^2 X^2+X+1 1 X^3+X^2 X^2 X 1 X^3+X+1 1 1 X 1 X^2 X^2+X X+1 X X^3 1 X^3+1 1 1 1 X^2 1 X^3+X^2 0 0 1 X+1 X^3+X+1 X^3 X^2+X+1 1 X^2+X 1 X^3+X^2+1 X^3+X^2+X X^2+X X^3+1 X^3+X^2 1 X^3+1 X^3+X^2+X X^2+1 0 1 1 X^3+X X^2+X+1 X^3+X^2+X+1 X+1 X^2 X^3+X^2+X X^2 X^3+X+1 1 X^3 X^2+X+1 X^3+X^2+X+1 X^3+X X^2 X^3+1 X X^2+X+1 X^3+X^2+X X^3 X^3+1 X X^3+X^2+1 X^3+X+1 X^2+X+1 X^2+1 0 X^3+X^2+X+1 1 X^2 X^2 X+1 X^2+1 0 X^2+X 1 1 X^2+X+1 0 X^3 X X^3+X X^3+X^2+1 X^3+X^2 X^3+X^2+1 X^3+X X^2 X^2+X+1 1 X^2+X 0 X 0 X^3+X^2+1 X+1 X^2+1 X^3 X^2 X^3+X 1 X^3+X^2+X+1 X X^3+X X^3+X^2+X X^3 X^2+X 1 X^3+X^2+X X 0 0 0 X^2 X^2 0 X^2 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^2 0 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 0 X^2 0 X^3 X^3 X^3 0 X^3 0 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 X^3 0 X^2 0 X^3+X^2 X^2 0 0 X^2 X^3 0 X^3+X^2 X^3 X^2 X^2 0 X^2 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 0 X^2 X^3 X^2 X^3+X^2 X^2 X^2 0 X^3+X^2 X^2 X^2 X^3 X^3+X^2 generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+170x^84+806x^85+1293x^86+1882x^87+1724x^88+2092x^89+1855x^90+1656x^91+1282x^92+1200x^93+763x^94+676x^95+411x^96+244x^97+136x^98+104x^99+18x^100+42x^101+13x^102+2x^103+8x^104+1x^106+2x^108+3x^110 The gray image is a linear code over GF(2) with n=720, k=14 and d=336. This code was found by Heurico 1.16 in 11.1 seconds.