The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X 1 X X X X^2 X X 0 1 0 1 0 1 X 0 0 X^2 1 1 X 0 1 X X X^2 0 0 0 X 1 1 1 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X X X X 0 0 X X^2 X X X X^2 0 X^2 X X X^2+X X X 0 X X^2 X X X X X^2 0 0 0 X X 0 X^2+X X^2 X^2 X X X^2+X X^2+X X^2 X^2 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2 X^2+X X^2 X X X^2 X X^2+X 0 X X^2+X X^2+X X^2+X 0 X X^2+X X X^2 X X^2+X 0 X^2+X X^2 X 0 X^2 0 0 X X^2 X^2 X^2 X 0 X^2+X X X 0 X 0 X^2+X X 0 X X X X^2 0 X^2+X 0 X^2 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X^2+X X 0 X 0 X X 0 0 X^2 X^2 X X^2 X^2 0 X 0 X^2 X X X^2 X^2+X X^2 X^2+X X^2 0 X^2 X^2 X^2+X X X^2 X^2+X X X X X X^2+X 0 X X^2 0 0 X 0 X^2+X 0 X^2+X 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+106x^62+417x^64+68x^65+635x^66+264x^67+735x^68+700x^69+826x^70+1288x^71+964x^72+1744x^73+935x^74+1816x^75+923x^76+1312x^77+875x^78+664x^79+696x^80+268x^81+530x^82+64x^83+275x^84+4x^85+156x^86+64x^88+27x^90+17x^92+5x^94+2x^96+1x^98+2x^100 The gray image is a linear code over GF(2) with n=296, k=14 and d=124. This code was found by Heurico 1.16 in 24.5 seconds.