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 1 X 0 X X X 1 X 1 X 1 1 X^2 X X 1 0 0 1 X^2 X 1 1 X^2 1 X^2 1 1 1 X 1 X 1 0 X^2 1 1 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2+X X X^2 X^2+X X^2 X^2+X X X 0 X^2+X X^2 X^2 X X^2+X 0 X X^2+X 0 X^2+X X^2 0 0 X^2+X 0 X X^2 X^2+X 0 X^2 X^2 0 0 X^2 X^2+X X X X^2 X X^2 X 0 X 0 X X X 0 X^2+X X X^2+X X X^2+X X X^2 X^2 X^2+X X^2 0 0 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^2 X X^2+X X^2 X^2 X X X^2 X X X^2 X 0 X^2 X X^2 X X^2+X X^2+X 0 0 X^2 X^2+X X^2 X X X^2 X^2 X^2+X X X^2+X X^2+X X^2 X X^2+X X X 0 X^2 X^2 X X^2 0 X^2+X 0 X 0 X^2 X^2 0 X^2+X X X X 0 0 X^2+X X^2 X X X^2+X 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 0 X^2+X X^2+X X^2+X 0 X X X X^2+X X^2 X^2 0 X^2+X X^2 X^2 0 X^2 X^2 0 0 X 0 X^2+X X X^2 0 0 X X^2+X X^2+X X X^2+X X X^2 0 0 0 X^2+X 0 X^2+X X^2+X X^2 X 0 X^2 X^2 X^2+X X X^2+X X 0 X^2+X 0 X X^2 X^2+X X X^2+X 0 X X^2+X X^2+X 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X X^2 0 X^2+X X^2 X X^2 0 X^2 0 X^2+X 0 X X X^2+X X^2+X X^2 X^2 X 0 X X 0 X^2+X X^2 X^2 X 0 0 0 0 X^2+X X^2 X^2+X 0 X^2 X^2+X X^2+X X^2+X X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2 X 0 X^2+X X^2+X X^2 X 0 X^2+X X^2 0 X^2 X 0 X X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+186x^66+366x^68+44x^69+564x^70+172x^71+710x^72+344x^73+881x^74+460x^75+928x^76+496x^77+818x^78+324x^79+664x^80+136x^81+428x^82+68x^83+278x^84+4x^85+144x^86+104x^88+49x^90+20x^92+2x^94+1x^112 The gray image is a linear code over GF(2) with n=304, k=13 and d=132. This code was found by Heurico 1.16 in 7.12 seconds.