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 1 X 1 0 0 1 0 1 X^2 X^2+X 1 X^2+X 1 X^2 1 1 X^2 1 0 X^2+X X^2+X 0 1 1 X^2+X 1 X 1 0 X^2 1 0 1 1 1 1 X 0 1 1 1 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 1 X+1 X^2 X^2+X X^2+1 1 X^2+X 0 1 0 1 0 1 X^2+X X+1 1 1 X 0 X X^2+X 1 1 X 0 X X X X^2+X X^2+X+1 1 1 X^2 1 X^2+X+1 1 X X^2+X+1 X^2 1 0 X+1 1 0 0 0 1 0 0 0 0 1 X^2+1 1 1 X+1 1 X 1 X^2 X X+1 X^2+X+1 X^2+X+1 X+1 1 0 X^2 1 X X+1 1 X^2 1 X^2+1 X^2 X^2+X X X^2+1 X+1 1 X^2+X 0 X 0 1 1 1 1 X+1 1 X X+1 X^2+1 X^2 X+1 X^2+X X^2+X X^2 0 X^2 0 X^2+1 1 X+1 X 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 X^2 X X+1 0 X^2+X+1 0 X^2+X+1 X X^2+X X+1 X^2+1 1 X^2+1 X^2 1 X+1 X X+1 X+1 X 1 1 X^2+X+1 X^2+1 X+1 X X^2+X 1 X^2+X 0 X+1 X^2+1 0 X^2+X+1 0 X^2+1 X^2+X+1 0 X^2 1 1 X^2+X+1 1 X X^2+X 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 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+218x^53+500x^54+848x^55+1215x^56+1698x^57+2146x^58+2382x^59+2856x^60+2990x^61+3002x^62+3068x^63+2927x^64+2600x^65+2035x^66+1572x^67+1208x^68+718x^69+346x^70+236x^71+103x^72+30x^73+26x^74+22x^75+8x^76+2x^77+8x^78+2x^80+1x^82 The gray image is a linear code over GF(2) with n=248, k=15 and d=106. This code was found by Heurico 1.16 in 80.4 seconds.