The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 X 1 X^2 1 1 X X 1 1 1 X 1 1 X^2+X 1 0 X 1 X^2+X 0 1 1 X^2 X 1 0 1 0 1 1 X^2 1 X 1 1 0 1 0 1 1 X^2 1 0 1 1 1 1 1 1 X^2+X X^2 0 1 X^2 1 1 X^2 X^2 X 1 X^2+X 1 0 X 1 1 1 1 0 X 0 1 0 0 1 X^2+X+1 1 X^2 0 X^2 X^2+X+1 1 1 1 X^2 X+1 X^2+X 1 X^2+X+1 X X^2 1 X^2+1 1 1 X 1 0 X^2+X X^2+X 1 X X^2+1 1 1 X^2+X+1 X^2 X^2+1 1 0 X^2+X 1 1 1 X^2 X^2+X+1 1 X^2+X 1 X+1 X^2+X 1 X^2+1 X X+1 X^2+X+1 X X^2+1 X^2 X+1 1 1 X X^2 1 0 X^2+X 1 1 1 X^2+X+1 X X+1 X X^2 X^2+X X^2 X^2+X 1 0 1 0 0 1 1 X+1 0 1 X+1 1 X X+1 X 0 1 0 1 1 X^2 X^2+X X^2+X 1 X^2+X+1 X^2+X X^2+1 X^2+X X^2+1 X^2+X+1 1 X^2+X 1 X^2+X X^2+X+1 X+1 X^2+X X+1 0 1 X^2+1 X^2+X+1 X^2+X X+1 0 X^2+1 X+1 X^2+X+1 X X 0 1 X^2 X^2 X^2 1 1 X^2+1 1 X+1 X X^2+1 X+1 0 X^2+1 1 X^2+1 X^2 X^2+X 0 0 X^2 1 X+1 1 X^2+X 1 1 X^2+1 X X+1 X^2+X+1 X X+1 0 0 0 X X X^2+X X^2 X^2+X 0 0 X X^2 X^2+X 0 X X X^2 0 X^2+X 0 X^2 X^2+X X^2 0 X 0 X^2+X X^2+X X X^2+X 0 X X^2 X X 0 0 0 X^2 X X^2 X^2+X X 0 X^2 X^2 X^2+X X^2+X X X^2 X^2+X X X^2+X X^2 X 0 0 X X^2+X 0 X^2+X X^2 X X^2+X X 0 X 0 X^2+X X^2 X^2+X 0 0 X^2 X^2 0 0 X^2+X X^2 X^2+X X^2+X 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 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 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+134x^73+292x^74+462x^75+461x^76+554x^77+720x^78+670x^79+733x^80+656x^81+647x^82+582x^83+523x^84+446x^85+307x^86+322x^87+207x^88+160x^89+117x^90+64x^91+52x^92+32x^93+25x^94+8x^95+7x^96+2x^97+4x^98+4x^99 The gray image is a linear code over GF(2) with n=324, k=13 and d=146. This code was found by Heurico 1.16 in 4.26 seconds.