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 X X 0 1 0 1 X 1 1 X 1 X 1 X^2 X 1 1 1 1 1 X X X^2 X^2 1 1 1 X 1 1 1 X X 1 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 0 X^2+X X^2+X X^2+X X^2 0 0 0 X X^2+X X^2+X X^2 X^2 X 0 X^2+X X X X X X^2 X X^2 X^2+X X^2+X X X^2 X^2 X X^2+X X X^2+X X^2 X^2+X 0 X X 0 0 X X^2+X X^2 0 X^2+X X^2+X 0 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X 0 X^2 0 X^2+X X^2+X X^2 X^2+X X^2 X X^2 X^2 X X 0 X X^2 X 0 X^2+X X X X^2 X^2+X X^2 0 X^2+X X^2+X 0 0 X X^2 X^2 X^2 0 X X^2 0 X^2 0 X^2 X^2+X X X^2+X X^2 X^2 0 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^2+X 0 X X^2+X X X^2 X 0 X^2+X X^2+X X X^2 X 0 X^2 X^2+X X^2+X 0 X X X 0 0 0 0 X^2 X^2 X^2+X X X^2 X^2 X X X^2 X^2 X 0 X^2+X X^2+X X X^2 X X X^2 0 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 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 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 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 generates a code of length 63 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+36x^54+62x^55+141x^56+198x^57+208x^58+234x^59+297x^60+346x^61+362x^62+384x^63+369x^64+394x^65+319x^66+202x^67+148x^68+118x^69+64x^70+64x^71+51x^72+32x^73+24x^74+12x^75+11x^76+9x^78+2x^79+6x^80+1x^82+1x^94 The gray image is a linear code over GF(2) with n=252, k=12 and d=108. This code was found by Heurico 1.16 in 1.25 seconds.