The generator matrix 1 0 1 1 1 1 1 X 1 2X 1 1 1 1 1 2X X^2 1 1 1 1 X^2+X 1 1 1 2X^2 1 1 2X 1 1 1 1 1 1 2X^2+2X 2X^2+X 1 1 1 1 1 X 1 1 1 1 1 X^2+2X 1 2X^2 1 1 2X^2+X X X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 2X^2+X 1 1 1 X 1 1 1 2X^2 1 1 0 1 1 2 2X^2 2X+1 2 1 2 1 0 2X^2+2X+1 2X^2+2X+1 2X^2 X+2 1 1 X+1 0 2X^2+X+2 0 1 1 2X^2+2X+2 X^2 1 X^2+2 2X+1 1 2X+1 2 2X^2+X 1 X+2 2X^2+X 1 1 2X^2+2X+2 X^2+1 2X^2+1 2X^2+2X 2X^2+X+2 1 X^2+2 2X^2+X+1 2X^2+2X 2X^2+1 X+2 1 2 1 2X 2X^2+2X+1 1 1 1 2X^2+2X+2 X^2+1 X^2+2X+2 X^2+X+1 X^2+X+2 2X X^2+X 2X+1 2X^2+2X+1 0 1 2X^2+X 2X^2+2 1 1 2X+1 1 2X+2 X^2+2 X^2+2X 2X^2+2X X^2+2X X X+2 1 X^2+2X+1 X+2 0 0 2X 0 2X^2 0 0 X^2 X^2 0 2X^2 2X^2 2X^2 2X^2+X 2X^2+X X^2+2X X X^2+X X^2+2X X^2+2X 2X^2+X X^2+X X^2+2X X 2X^2+2X X X^2+2X X X^2+2X 2X X^2+2X X X^2+X 2X^2+X X^2+2X 2X^2+2X X^2 0 X^2+X 2X^2+2X X^2 2X 2X X 0 2X^2+X X 2X^2 2X^2+X 2X^2+X 2X^2+2X 2X^2 X^2 0 2X^2+X X X^2 2X^2 2X^2+X 2X^2+2X 2X^2+2X 2X X^2+X 0 2X 0 2X^2+2X X X^2+2X 2X^2 X X 2X^2+X 2X^2+X 2X 0 2X^2+2X 2X^2+2X 2X^2+2X X^2+2X 2X^2+2X 2X^2+2X 2X^2+X 0 0 0 X 2X^2+X X^2+X X^2 X X^2+2X X^2+2X 2X 0 2X^2+2X 2X^2+2X X^2+2X X^2+2X 2X^2 X^2+2X 0 2X^2 X^2 X 2X^2+X 2X^2 X^2+X 2X X^2+X 0 0 X^2+2X 2X 2X^2+X X^2+X X^2+X X^2+2X 2X^2+X X^2+2X 2X^2+X 2X 2X^2 2X^2+X X^2+X 2X^2+2X X^2 2X X X^2+X X^2 0 2X 2X^2+X 2X^2 X 0 X^2+2X X X^2+2X 2X^2+X 2X^2+X X^2+2X 2X 2X X 2X^2 2X^2+X X X^2+X X^2+2X X^2 2X 0 2X X^2 X^2+X X^2+2X X^2 2X^2 0 0 2X X^2 X^2 0 generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 156. Homogenous weight enumerator: w(x)=1x^0+696x^156+558x^157+990x^158+2340x^159+1656x^160+2430x^161+4256x^162+3708x^163+3888x^164+5952x^165+4698x^166+5346x^167+5700x^168+5202x^169+3834x^170+3402x^171+1530x^172+972x^173+930x^174+144x^175+36x^176+360x^177+252x^180+102x^183+42x^186+18x^189+6x^192 The gray image is a linear code over GF(3) with n=747, k=10 and d=468. This code was found by Heurico 1.16 in 23.6 seconds.