The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 1 X 1 1 X^2 1 1 0 1 1 X 1 1 X^2+X 1 1 1 1 X^2+X 1 X^2+X 1 1 1 X^2 1 1 0 1 1 X^2 1 1 1 1 X^2+X 1 1 1 X^2+X 1 1 X^2+X 1 X^2+X X 1 1 1 0 1 0 X^2 0 1 1 0 1 1 X^2+X X^2+X+1 1 0 X+1 1 X 1 X^2+1 X X^2+X+1 1 X^2 1 1 0 1 1 X^2+X X+1 1 X^2+X 1 1 X^2 X+1 X X+1 1 X+1 1 X^2+1 X^2+X X 1 X^2 1 1 X^2+X 0 1 X^2 X^2+X+1 0 X^2+1 1 X^2+X+1 X^2+X X^2+X 1 X^2 X^2+X 1 X^2+1 1 X^2 1 X^2+1 X^2+1 1 X 1 1 1 X^2+X+1 0 0 0 X 0 X^2+X 0 X^2+X X^2 X X X X^2 X^2+X X X^2+X X^2+X X X 0 0 X^2 0 X^2 X X^2+X X^2+X 0 X^2+X 0 0 X^2+X X^2+X X^2+X X^2+X 0 X^2 X X^2 X^2+X X^2+X X^2 0 X^2 X X^2 X^2 X^2 0 X^2 X^2+X 0 0 0 X^2+X X^2+X X X^2 X^2 X^2+X X^2 X 0 0 X^2+X X^2 0 0 X^2 X 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+178x^62+84x^63+390x^64+136x^65+485x^66+188x^67+524x^68+224x^69+550x^70+172x^71+462x^72+136x^73+254x^74+68x^75+122x^76+16x^77+54x^78+23x^80+13x^82+8x^84+2x^86+4x^88+2x^92 The gray image is a linear code over GF(2) with n=276, k=12 and d=124. This code was found by Heurico 1.16 in 35.8 seconds.