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 X 0 1 X^2 1 1 1 1 0 1 0 X 1 X 0 1 1 X 1 1 X^2 1 1 X^2 X^2 1 X X 1 1 X X 1 X X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2+X X^2 X^2+X 0 X^2 X^2+X X X^2 X^2+X X 0 X^2 X^2 X^2+X X^2 X^2 X^2+X X^2 0 X X^2+X X X^2 X^2 X^2+X X^2 X^2+X X^2 X^2+X 0 0 X^2 X^2 X X X^2 X^2+X X^2 X^2 X^2+X X^2+X 0 X^2+X 0 0 X^2+X 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X X^2 0 X^2+X X^2+X X^2 X^2+X X^2 0 X^2 X 0 X X 0 X 0 X 0 X^2+X X 0 0 X X X^2 X^2+X X^2+X X^2 X^2 X^2 X X 0 X X^2+X X^2+X 0 X 0 0 X X^2+X X X X^2 0 X X X^2 X X^2 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 0 X^2+X 0 X X^2 X X 0 0 X X^2 X^2+X X X X^2+X X^2 0 0 X X^2+X X^2+X 0 0 0 0 0 X^2 X X^2+X X^2+X X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X X 0 X^2 X X X^2+X 0 0 X^2 X^2 X^2 0 X X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 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 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+198x^60+24x^61+280x^62+68x^63+436x^64+176x^65+436x^66+260x^67+524x^68+224x^69+432x^70+172x^71+296x^72+80x^73+174x^74+12x^75+154x^76+8x^77+78x^78+43x^80+6x^82+11x^84+2x^86+1x^100 The gray image is a linear code over GF(2) with n=272, k=12 and d=120. This code was found by Heurico 1.16 in 46.6 seconds.