The generator matrix 1 0 0 0 0 1 1 1 2X 1 1 1 1 1 0 1 0 1 1 X 1 1 0 1 X 1 1 1 X 1 1 1 1 1 1 1 1 2X 1 1 1 2X 1 0 0 1 1 1 X X X 1 1 1 1 1 X 1 X 1 1 0 1 1 1 1 1 1 X 1 1 1 X 0 1 1 1 X 1 1 1 0 1 0 0 0 2X 1 2X+1 1 0 X 2X+2 2 1 1 2X+2 1 2 1 1 2X+1 X+2 0 2X 1 X+1 X+2 2X+1 0 2X 1 2X+1 1 2X+2 2X 0 0 X 2X+2 X X+2 1 X+2 1 1 2 2X 0 1 1 1 X+1 2X+2 0 2X+2 X+2 1 X+2 2X 1 X 2X 2X+1 0 2X 2 X 2 1 X+2 2 2X 0 0 1 2X+2 X 1 0 2 2X 0 0 1 0 0 0 0 0 0 X X X X 2X 2X 2X X 2X 2X X 2X 2X 2X 2X 2 X+2 2X+1 X+2 1 1 X+1 X+2 2 X+1 2X+2 1 X+2 1 X+2 2X+2 X+2 2X+2 X+2 X+1 2X+1 X+1 2 2X+2 2X+2 2X+2 X+1 1 0 2X+1 1 2X+1 1 X+2 1 2X+1 1 1 1 1 2 2X+2 1 X+2 X+2 X+1 2X 0 1 1 2X+2 X+2 2X 2 2X+2 X 0 0 0 0 1 0 2X+1 1 2X+2 X+1 X+1 X+2 2X 2X+1 0 2 X+2 2 2X+2 2X 1 X+2 X 1 0 X+1 2 2X X+1 X+1 2 X+1 2X+1 X 1 2 2X+1 2X 2X+2 2X+1 2X+1 2X+2 2 2X+1 X+1 X+2 X+2 1 1 X+2 0 1 X+1 X X X+1 2X+1 X+1 2X 2X+2 X 2X+2 2X X X+1 2X 2 X+2 X 2 X+2 2X+1 1 X+2 2X+1 2X+2 2X+1 0 X 0 X+1 2X+1 0 0 0 0 1 2X+2 X X+2 X+2 2X+1 X X+1 2X X+1 2X+1 2X+2 0 2X 0 2X+1 2X+1 2 2X+1 2 0 2X X X+1 2 2X+1 2X+2 0 X+1 2X+1 1 2 0 X+2 2 1 X+1 2X 2X 1 X+1 1 2 2X X+2 1 0 2X+1 2X 1 0 X+1 2X+2 1 2X 2X+2 2 X+1 0 X+1 1 X+2 0 2 X+2 X+2 2X+2 2X 2X+1 2X 2X+2 X+1 X 2X+1 X 2X 2 generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 145. Homogenous weight enumerator: w(x)=1x^0+168x^145+252x^146+408x^147+918x^148+582x^149+1270x^150+1830x^151+1020x^152+1632x^153+2556x^154+1458x^155+2110x^156+3090x^157+1566x^158+2998x^159+3768x^160+1824x^161+2962x^162+3924x^163+2028x^164+2724x^165+3588x^166+1776x^167+2392x^168+3096x^169+1230x^170+1692x^171+1866x^172+864x^173+978x^174+948x^175+378x^176+342x^177+360x^178+120x^179+146x^180+108x^181+24x^182+26x^183+24x^184+2x^198 The gray image is a linear code over GF(3) with n=243, k=10 and d=145. This code was found by Heurico 1.16 in 66.3 seconds.