The generator matrix 1 0 0 0 1 1 1 1 1 1 1 X X X^2 X^2+X 1 X^2 1 X^2 1 0 X 1 0 1 0 X^2 X^2 X^2+X 1 1 1 1 1 X^2+X 1 X^2+X 1 1 1 1 X^2 X 1 0 1 X^2+X X^2+X X^2 0 1 1 X^2+X 1 X 0 X^2 1 X^2 1 1 0 1 0 1 0 0 X 1 X^2+X+1 X^2 X^2+X X+1 X^2+1 1 1 1 X X^2 1 X^2+1 1 X^2 X^2 X^2+X X+1 X^2+X X^2+X 1 1 1 1 X+1 1 X^2+1 0 X^2+X 1 X^2+X+1 1 X^2+X X X^2 1 1 1 X^2+X+1 1 X^2 1 1 X^2 1 X^2 X^2+X 1 X^2+1 1 X^2 X^2+X X^2 0 X^2 1 1 X+1 0 0 1 0 0 0 0 1 X^2+1 1 1 X+1 1 X 1 X^2 X X^2 X^2+X+1 X+1 X 1 X^2+X+1 1 X^2+1 X X^2 X^2+X+1 X^2+X X+1 X^2+X X^2 X^2+1 X^2+X X^2+1 1 X^2 X X^2+X+1 X^2+X+1 0 X^2+X+1 X+1 X^2+X+1 1 X^2 1 X^2 1 0 X X X^2+X X^2+1 X+1 1 1 0 1 X+1 X 0 X+1 0 0 0 1 1 X^2+X+1 X^2+X X+1 0 1 X^2+X 1 X^2 X+1 1 X^2+1 X^2 1 X 0 1 X^2+X+1 X+1 0 X+1 X X^2+X+1 X+1 1 X X^2+X+1 X^2 X^2+X X+1 X^2+X X+1 0 0 X+1 X+1 X^2 X^2+X X+1 X^2+X X X^2+1 X^2+1 X^2+1 1 X^2+X X^2+X X^2+X X+1 X^2+X X+1 X^2+1 X^2+X X^2+X+1 X+1 X X^2+X X X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 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 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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+254x^54+440x^55+892x^56+1188x^57+1850x^58+2032x^59+2533x^60+2520x^61+3188x^62+2976x^63+3240x^64+2720x^65+2674x^66+1904x^67+1578x^68+1032x^69+804x^70+456x^71+306x^72+92x^73+50x^74+25x^76+9x^78+1x^80+2x^82+1x^94 The gray image is a linear code over GF(2) with n=252, k=15 and d=108. This code was found by Heurico 1.16 in 41.7 seconds.