The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 X 1 0 1 1 1 0 1 1 2X X 2X 1 1 1 1 1 1 0 1 1 0 1 0 0 2X 0 X X 1 2X+2 X+2 2X+1 X+2 1 2X+2 2 1 2X+2 X+1 2 X+1 1 X+1 1 X 1 2X 2X 2 1 X+1 X 1 1 X 2 2 X+1 2X+2 X+2 X X 2X 0 0 0 1 0 0 X 2X+1 2 2 2X+2 2X 2X X+1 2 X+2 X+2 2X+1 X+1 X+2 0 2X+1 X+2 2X X+2 2X+2 2X X+1 2X+2 1 1 1 1 2X+1 1 1 2X+1 2X+2 X 2X+2 2X+1 2 1 X+1 X+1 0 0 0 1 2X+1 2X+2 2X+1 1 X+1 X+1 X+2 2X+2 2 2X+1 2X 2 X 0 X X X+1 X+2 1 2 2X X+1 2X 2 2X+1 2X+2 X+2 2 X+1 2X X+2 2X 1 0 0 X 0 X+2 2X+1 0 generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+174x^79+282x^80+236x^81+396x^82+450x^83+382x^84+504x^85+504x^86+348x^87+420x^88+408x^89+278x^90+396x^91+336x^92+260x^93+276x^94+270x^95+132x^96+198x^97+156x^98+64x^99+54x^100+24x^101+12x^103 The gray image is a linear code over GF(3) with n=132, k=8 and d=79. This code was found by Heurico 1.16 in 0.438 seconds.