The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 1 X 1 1 X 0 1 1 X 1 1 1 1 X^2 1 1 X 1 1 X^2 1 1 X^2 1 X 1 1 X 1 1 1 X^2 X^2+X 0 1 X^2 1 1 1 X 1 1 1 1 X 1 X^2+X 1 1 1 1 X X^2 1 1 X^2 1 1 X^2+X 1 0 1 1 1 1 0 1 1 0 X^2+X+1 1 X+1 X^2+X 1 X^2 X^2+1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X 1 X^2+1 X X^2+1 0 1 X^2+X X^2+1 1 X^2+X+1 0 1 1 X+1 1 X 1 X^2+X+1 0 1 X+1 X^2+X+1 X^2 1 1 1 0 1 X X^2+X 1 1 X+1 X^2+1 X X 1 0 1 X^2+X+1 X+1 0 X+1 1 1 X^2+X+1 X^2+X 1 X X^2 1 X 1 X^2+1 1 X X^2+X+1 0 0 X 0 X^2+X 0 X^2 X^2 X X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X^2+X X^2+X X X^2 0 X^2+X X X^2 X^2+X X^2 X 0 X^2 X X^2+X X^2 0 X^2+X X^2 X X^2+X X X X X X^2 X^2 0 0 X X X^2 0 X X^2 X^2+X 0 0 0 0 X^2 X^2+X X 0 X^2+X 0 X^2+X X^2+X X^2 X^2+X X X^2+X X^2 X^2+X X^2+X X 0 X X^2+X 0 0 0 X 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2+X X^2+X X X X^2+X X X^2+X X^2+X X^2+X X X 0 X^2 X X^2 0 X 0 X X^2+X X^2 X^2+X X X^2+X 0 0 X^2+X 0 X 0 0 X^2+X X X^2 X^2+X X^2 X^2+X 0 X^2+X X^2+X X^2 X 0 0 X X^2 X X^2+X X^2 X^2 0 0 X^2+X 0 X^2 X^2 0 X^2+X X X X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+177x^68+112x^69+330x^70+272x^71+413x^72+272x^73+428x^74+224x^75+430x^76+272x^77+324x^78+272x^79+249x^80+112x^81+102x^82+40x^84+24x^86+23x^88+6x^90+6x^92+2x^94+2x^96+3x^100 The gray image is a linear code over GF(2) with n=300, k=12 and d=136. This code was found by Heurico 1.16 in 1.28 seconds.