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 X 1 0 1 1 1 X 1 X 1 X^2 0 1 1 1 0 1 X 1 1 1 X^2 1 X X^2 0 1 0 1 1 1 X 0 1 X^2 1 X 1 1 1 1 1 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2+X X X^2 X X X^2 X^2+X X^2 0 0 X^2+X X X X X^2 X^2+X X^2 X^2 X X^2+X X X X 0 X^2 X X X^2 X X^2+X X^2+X 0 X 0 X^2 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X X X^2+X X 0 X^2 X X 0 X^2+X 0 0 0 0 X X X X^2+X X X^2 X 0 X X^2+X X X^2 0 0 X^2 X X X^2+X X^2 X X X^2 X X^2 X^2+X 0 0 X^2 0 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X 0 X^2 X^2 X^2+X X X X 0 X X^2+X X^2+X X^2 X^2+X X X^2+X X^2+X 0 X^2+X 0 0 X X^2 X^2 0 X^2+X X^2 X^2 0 X X^2+X 0 0 X^2+X 0 0 X^2 X^2+X X 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X 0 X^2+X 0 X 0 X^2+X X X^2 X X 0 X^2 0 X^2 0 0 X^2 X^2+X X^2 0 X 0 0 X X^2+X X^2 X^2+X X^2 X^2+X 0 X X X X^2+X X X^2+X X^2 X X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 67. Homogenous weight enumerator: w(x)=1x^0+50x^67+96x^68+152x^69+181x^70+218x^71+260x^72+274x^73+338x^74+352x^75+408x^76+392x^77+307x^78+256x^79+191x^80+148x^81+109x^82+92x^83+72x^84+48x^85+37x^86+44x^87+24x^88+10x^89+17x^90+10x^91+4x^92+2x^94+2x^95+1x^118 The gray image is a linear code over GF(2) with n=304, k=12 and d=134. This code was found by Heurico 1.16 in 1.7 seconds.