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 1 X^2+X X^3+X^2 1 1 1 1 X^3+X 1 1 0 1 1 X^2+X X^3+X^2 1 1 X^3+X 1 1 0 1 1 1 1 X^2+X 1 1 X^3 1 1 X^3+X^2+X 1 1 X^3+X^2 1 X 1 X 1 X 1 1 1 1 0 X^3+X 1 X^3 X 1 1 X 1 X^3+X^2 X 1 0 X 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 X^2+1 1 1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 1 X^3+X X^3+X^2+X+1 1 X^3+X^2 X^3+1 1 0 X+1 X^2+X X^2+1 1 X^3 X^3+X+1 1 X^3+X^2+X X^3+X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+X^2 X^2 0 0 X^3 X^3+X^2 X^2+X X^3+X X^3+X^2+X X 1 X^3+1 1 X^2+X 1 X^3+X^2 X^3+X X^2+X+1 X 1 X^3 X^2 X^3+X^2 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 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 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 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 X^3 0 X^3 0 X^3 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+252x^70+208x^71+543x^72+368x^73+535x^74+384x^75+515x^76+384x^77+439x^78+176x^79+204x^80+16x^81+37x^82+15x^84+16x^86+2x^92+1x^118 The gray image is a linear code over GF(2) with n=600, k=12 and d=280. This code was found by Heurico 1.16 in 107 seconds.