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 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 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 0 X 2X 0 2X^2+X 2X X^2 X^2+2X 2X^2+X 2X^2+X 2X 0 X^2 2X^2+X 2X X^2+2X 0 X^2 X^2+X 2X^2+X 2X X^2+2X 2X^2+2X X^2+2X X^2+X 2X^2+X X^2+X X^2 X^2+X 2X^2 X^2+X 2X^2+X X^2+X 2X^2+X X^2+X X^2+X X 2X 2X X^2+2X 2X X^2+2X X^2+2X 2X^2+2X 2X^2+X 0 0 0 X^2 X^2 2X^2 2X^2 0 0 2X^2 2X^2+2X 2X X^2+2X 2X X^2 2X^2 2X X^2 X^2 X X X 2X^2 2X^2+2X X^2+2X 0 X 0 2X^2+X 2X^2+2X X^2+2X X^2 2X^2+X X X^2 X^2+2X 0 0 X^2 0 0 0 0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 X^2 2X^2 X^2 0 2X^2 0 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 2X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 X^2 2X^2 2X^2 0 X^2 0 2X^2 X^2 0 X^2 2X^2 X^2 X^2 0 2X^2 0 X^2 0 0 0 2X^2 2X^2 0 2X^2 0 X^2 2X^2 0 0 0 X^2 0 0 2X^2 0 0 0 0 0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 0 X^2 2X^2 0 0 X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 0 2X^2 0 2X^2 0 2X^2 0 2X^2 0 X^2 0 2X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 0 2X^2 0 X^2 0 X^2 2X^2 0 0 0 0 2X^2 2X^2 0 X^2 2X^2 X^2 2X^2 X^2 2X^2 0 2X^2 0 X^2 2X^2 0 X^2 X^2 0 2X^2 X^2 0 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 2X^2 0 0 X^2 X^2 2X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 2X^2 2X^2 2X^2 0 0 0 X^2 2X^2 0 2X^2 X^2 0 0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 0 0 0 X^2 0 2X^2 generates a code of length 81 over Z3[X]/(X^3) who�s minimum homogenous weight is 154. Homogenous weight enumerator: w(x)=1x^0+150x^154+84x^155+58x^156+168x^157+348x^158+84x^159+1614x^160+324x^161+62x^162+3054x^163+48x^164+30x^165+126x^166+60x^167+6x^168+84x^169+66x^172+30x^173+18x^175+78x^176+30x^178+24x^181+12x^184+2x^237 The gray image is a linear code over GF(3) with n=729, k=8 and d=462. This code was found by Heurico 1.16 in 20.2 seconds.