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 X^2 X X 0 X X 0 1 0 0 1 1 1 1 X 1 1 0 1 X X 1 X X 1 1 1 1 1 X 0 1 X^2 X 0 0 1 X 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X X^2 X^2 X^2+X X^2 0 X X^2 X 0 X X^2+X 0 X^2 X 0 X 0 0 X^2 X X^2 X^2+X 0 X^2+X X^2+X 0 X^2 X 0 0 X X X X^2 X^2 X^2+X 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X X^2+X X 0 0 X X^2 0 X^2 X 0 X^2 X^2+X 0 0 X X^2 X 0 X^2 X^2 X X^2+X X X X 0 X X^2+X X^2 X 0 0 X^2 X X X^2 X^2+X 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X 0 0 X^2+X X X 0 0 X X^2 0 0 0 X^2+X X 0 X X^2 0 0 X^2+X X 0 X^2+X X X^2+X X^2 X^2 0 X^2 X^2+X X^2+X 0 X^2+X 0 0 X^2+X X^2+X X^2 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X^2+X 0 X^2+X 0 0 0 X X X X^2+X 0 0 0 0 X^2 X X 0 X^2 X^2 X^2 X X^2 X X^2+X X^2+X X^2 X^2 0 0 0 X^2+X 0 X^2+X 0 X X^2+X X 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X^2 X^2 0 X^2 X^2+X X X^2 0 X 0 X^2 0 X^2 X X X^2 X^2+X X^2 0 X X^2+X X X^2+X X X^2+X X^2 0 X^2 X^2 X^2 X^2 X^2 X^2+X 0 X^2+X X X^2 X^2 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+168x^66+361x^68+92x^69+606x^70+156x^71+766x^72+328x^73+860x^74+372x^75+859x^76+552x^77+830x^78+324x^79+609x^80+168x^81+454x^82+44x^83+293x^84+12x^85+172x^86+104x^88+38x^90+14x^92+8x^94+1x^108 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 6.92 seconds.