The generator matrix 1 0 0 1 1 1 X X^3+X 1 1 1 X^3+X^2 1 X^3+X^2+X 1 1 X^3 1 X^2 1 0 1 X^3+X X^3+X^2+X 1 X^3+X^2 1 1 X^3+X^2 1 X^3 X^2+X 1 1 1 1 1 1 0 1 X^2+X X^3+X^2+X 1 1 X^3 1 X^2 1 X X X^2 1 X X^2+X 0 1 X^3 1 1 X^3+X^2+X 0 1 X^3+X^2 1 1 X^3 1 X^3+X X^2+X X 1 1 0 X^2+X X^3 1 1 1 0 1 0 0 X^2+1 X+1 1 X^3 0 X^3 X^3+1 1 X^3+1 1 X^3+X^2 0 1 X^2+1 X^2+X X^3+X^2+X+1 1 X^2 1 1 X^3+X^2+1 X^2+X X^3+X^2+1 X 1 X^2+X X 1 X X^3+X^2+1 X^3+X^2+X+1 X^3+X+1 X^3+X X^3+X+1 1 X^3+X^2+X X^3+X X X^2+X+1 X^3+X 1 X^2+X+1 0 X^2+1 1 X^3+X^2 1 X^3+X X^3+X^2+X 1 1 X^2 1 X^3+X^2+X X^2 X^3+X^2+X 1 X^3+X 1 X^3+X^2+X+1 X^3+X+1 1 X X^3 1 0 X^3 X^3+X^2+X+1 1 1 1 X^3+X^2+X+1 X^3+X^2+X+1 0 0 0 1 1 1 0 X^2+1 1 X X^3+X^2+X+1 X^2+X X+1 X^3+X^2+X+1 X^3+X^2 X^3+1 X^2 X^3+X^2+X X^2+X 1 X^2+X+1 X^2+X+1 X^3+X^2+X+1 X^3+X X^2+1 X^2+1 1 X^3 X^3 X^3+X^2+X X^3+1 1 X^3+X+1 X X^3+X+1 X^3+X X^3+X^2+1 X^2+X+1 0 1 X^2 1 1 X^3+1 X^2+1 X^2+X X^2+X+1 1 X^3+X^2 X^3+X 1 X^3+X^2+X+1 X^2+1 1 X^3+X^2+1 0 X^3+X^2+X X^3+X^2 0 X^2 1 1 X^2+X+1 X X^2+X X^3+X+1 X^3+1 X^3+X^2+X+1 1 X^2 X^3 X^3+1 X^3 X^3+X^2+1 X+1 X^3+X+1 X^3+X^2+X 1 0 0 0 0 X X^3+X X^3 X^3+X X^3+X X^3+X X X^3+X^2+X X^3 X^2 X^2+X X^3+X^2 X^2+X X^2 0 X^3+X^2 X^2+X X^3+X X^3 X^2+X X^3+X^2 X^3+X^2 X^3+X X^2+X X^3+X^2 X X^2 X^3 X^2 0 X^3+X X^3 0 X^3 X^3+X^2+X X^2+X X^2+X X^3+X X^3+X^2 X^3+X X 0 0 X^3+X^2+X X^2 0 0 X^2 X^2+X X^3+X^2+X 0 X^3+X^2 X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2 X X X^2+X X^2 X^3+X^2 X^3 X^2+X X^2+X X^3+X^2 X X^3 X^3+X X^2 X X^3+X^2+X X^3 X^2+X 0 generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 71. Homogenous weight enumerator: w(x)=1x^0+122x^71+802x^72+1344x^73+2316x^74+3116x^75+3286x^76+3898x^77+3867x^78+3620x^79+3281x^80+2704x^81+1848x^82+1114x^83+675x^84+390x^85+219x^86+46x^87+58x^88+12x^89+22x^90+14x^91+9x^92+4x^93 The gray image is a linear code over GF(2) with n=624, k=15 and d=284. This code was found by Heurico 1.16 in 13.1 seconds.