The generator matrix 1 0 0 1 1 1 0 X^3 1 1 X^3 X^2 1 1 1 1 X^3+X X^3+X 1 X^3+X^2+X 1 X^3+X X 1 X^3+X 1 1 1 X^3+X 1 1 1 X^2+X 1 1 X^3+X X 1 X^3+X^2 1 X^2 1 1 0 1 1 1 0 1 X^3+X^2 1 X^2 1 X^2 X^2+X 1 0 1 1 1 1 1 1 1 1 X 1 X^3 1 1 X^3 1 X^3+X^2 1 X^3+X^2+X 1 X^3+X^2+X 1 1 X^2 1 1 1 1 1 1 0 1 0 0 X^2+1 X^2+1 1 X^3+X^2+X X^3 X^3+X^2+1 1 1 X^3+X^2 1 X^2+X X+1 1 X^2+X X 1 X^3+X^2+X+1 1 1 X^3+X^2+X+1 X^2 X+1 X X+1 1 X^2 X^3+X^2+X X^3+X^2 1 X^3+1 X^2+1 X^3+X 1 X^2+X+1 0 X 1 X^3+X+1 X^2 1 X^3+X^2+X X^3 X^3+X 1 X^3+X^2+1 1 X^2+X+1 1 1 X^3+X 1 X^3+X^2+X+1 X^3+X X^3+1 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2+X+1 X^3+X^2 X^2+X 0 0 X^3+X X^3+X^2+X X^2+1 X^3 X^2 X^3+X^2+X+1 1 X^2+X+1 1 X+1 1 X^3+X X^3+X^2+1 1 X^3+1 X^3 X^3+X^2+1 X^3+X^2 X^3+X 0 0 0 1 X+1 X^3+X+1 X^3 X^3+X^2+X+1 1 X^3+X^2+X X^2+1 1 X^3+X X^3+X^2+1 X X^3+X+1 X^2 X^3+X^2+1 1 X X^2 X^2+X+1 X^3+X^2+X X+1 X^2+1 1 X^2+X X^2 X^3+X^2+X+1 X^3+X^2+X+1 X+1 X^2+1 X^3 1 X^3+1 X^3+X 1 X^2+X 0 1 X^3 X^2+1 X^2+1 X^3+X^2+1 X^3+X^2+X X^3+X^2+X+1 X^2 X^3+X^2+X X^2 X^3+X^2+X+1 X+1 X X^3+X X^3 1 X^3+X^2+1 X^3+X^2+1 1 X^2+1 1 X^2+X X^3+X^2+X+1 X+1 X^3+X^2+X+1 X^3+X X^2+X 1 X^3+X^2+1 1 X^3+1 X^3+1 1 X^2+X X^2+X+1 1 X^2+X+1 0 X^3+X^2+1 X^3+X^2+1 X^3+X^2+X+1 X^3+X^2+X X^3+X+1 X^3+X+1 X^3+X X^3+1 X^3+1 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+114x^81+688x^82+1192x^83+1147x^84+1006x^85+953x^86+794x^87+653x^88+438x^89+405x^90+268x^91+189x^92+142x^93+97x^94+74x^95+24x^96+4x^97+1x^98+2x^108 The gray image is a linear code over GF(2) with n=688, k=13 and d=324. This code was found by Heurico 1.16 in 16.3 seconds.