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 X 0 X^2 0 X^2 X^2 1 1 1 0 1 X X 0 1 1 X^2 1 X 1 X^2 X^2 1 1 0 X^2 1 X 1 X X^2 0 1 X X 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2+X 0 X X X^2+X X^2 X^2+X X^2 X X^2+X X^2+X 0 X^2+X X^2+X 0 X X^2 X^2 0 0 X^2+X X^2 0 X^2 X^2 X^2 X^2 X X X X^2+X X^2 X X^2+X X^2+X X 0 0 X X 0 0 X X^2 X X^2+X X X^2 X^2 X 0 X^2+X X 0 0 X^2 X 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X X^2 X^2+X X X^2 0 X^2 0 X^2 X^2+X 0 X^2+X X^2+X 0 X^2 X^2+X 0 0 X^2+X X^2+X 0 X^2+X X X X X X X X^2 X X 0 X^2+X 0 X^2 X^2 X^2+X X^2+X X X^2 X^2 X^2+X X X^2 X^2 X^2 X^2+X 0 X^2 0 X X X^2+X X X^2+X X^2+X 0 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X 0 X X X^2+X 0 X^2+X X X^2+X X^2+X X^2 0 X^2+X X X^2 X^2 X^2+X X^2+X 0 X^2 0 0 X^2 X^2 0 X 0 X^2 X X^2+X X^2 X^2 X X X^2 X^2 X^2+X X X^2+X 0 X X^2 X^2 X X X^2 X X X X 0 X 0 X^2 0 X X X^2+X 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X X 0 X 0 0 X^2+X X X^2 X^2 0 X^2+X 0 X^2+X 0 X^2 0 X^2+X X X X X^2 0 X X^2 X^2 0 X X X X X 0 0 0 X^2+X X^2 X X^2 X^2+X X X^2+X X X X^2+X X^2+X X^2+X X X X X^2 0 X 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 0 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+167x^62+4x^63+359x^64+52x^65+581x^66+160x^67+754x^68+344x^69+833x^70+448x^71+970x^72+472x^73+778x^74+368x^75+611x^76+152x^77+498x^78+44x^79+291x^80+4x^81+170x^82+68x^84+42x^86+15x^88+3x^90+2x^92+1x^100 The gray image is a linear code over GF(2) with n=288, k=13 and d=124. This code was found by Heurico 1.16 in 6.63 seconds.