The generator matrix 1 0 0 1 1 1 1 1 1 2X 0 1 1 1 1 2X 1 1 1 1 1 1 X 2X X 1 1 1 1 1 1 1 1 2X 0 X 1 X 1 1 1 1 1 0 1 1 1 1 1 1 2X 2X 1 X 1 1 1 1 1 X 1 2X 1 1 1 1 1 1 1 1 0 1 1 1 2X 1 1 1 1 2X 0 X 1 1 1 1 1 X 1 1 0 1 0 0 0 1 2 1 2X+1 1 1 2 2X+2 2 2X+2 1 1 2X 2X+2 1 0 X 1 1 0 2X+1 2X 2 X 2X+1 2X+2 0 2X+1 1 1 1 X+2 2X 2 X+2 2X+1 2 X+1 2X X+1 0 1 X+1 2 X+1 1 1 1 1 2 X+2 0 2X+2 2X 1 X X 2X+1 2X 2X+1 2 2X+2 2X+1 2X+2 2 1 2X+2 X+2 0 0 2X+1 2X+1 X X 1 1 1 X X X X+1 1 1 2X 2 0 0 1 1 2 2 X+2 X+1 2X 2X+1 2 0 2X+1 X+2 0 X+2 X+1 2X+1 2X+1 X+2 2 2X 1 2X 1 0 2X X+2 2 0 2X 2X+1 2 2X+1 X+2 2X 0 1 2X+2 X+1 2X X+1 2X+2 1 2X 2X+2 2X+1 2X+1 X X 2 2 2X 2X+2 1 2X+1 2X 2X+2 0 2X+1 2 1 2 X+1 X+1 X 1 2 1 2X+1 2X+1 X+2 X+2 0 1 2X+2 2 X+2 X+2 X 2X X 2X 2X+1 1 2X+1 X+1 0 2X+1 X 0 0 0 2X 0 0 0 2X 0 2X 2X 0 X 2X X X 2X X 0 X 2X X 0 2X 0 2X X 0 0 0 2X 2X X 2X 0 0 2X X 2X 2X 2X 0 0 2X X X X X 2X X 0 X 0 X X 2X X 0 2X 0 X 2X X 0 0 X 0 2X 0 2X X 0 2X X 0 2X X 0 2X 2X 0 X 2X X X 2X X X 0 X 0 0 0 0 X 0 2X 0 0 2X 2X X X X 0 2X X 2X X X X 2X 0 2X 2X X 0 2X 2X 0 2X 0 X 0 2X 2X 2X 0 0 2X 0 X X X 0 0 X X X 2X X X X 2X 2X X X X 2X 0 0 X 0 2X X 0 2X 2X 2X 0 2X 0 X 2X 0 0 2X 0 0 0 0 0 2X 0 2X X 0 X 0 X 0 0 0 0 0 2X X 0 0 2X 2X 2X 2X 2X 0 0 X 0 0 X 2X X 2X X 2X 0 2X 2X 0 2X 2X 2X 2X 2X 2X 0 0 2X 0 X 2X X X 0 0 2X 0 X X 0 0 X 0 X 0 2X 2X 2X 2X X 0 X 2X X 0 2X 0 X 2X 0 2X X 0 0 2X X 0 2X 2X 2X X 2X 0 X X 0 2X 2X 0 X generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 165. Homogenous weight enumerator: w(x)=1x^0+236x^165+138x^166+270x^167+694x^168+318x^169+402x^170+1108x^171+510x^172+414x^173+1380x^174+552x^175+612x^176+1418x^177+654x^178+672x^179+1444x^180+594x^181+540x^182+1474x^183+504x^184+522x^185+1236x^186+498x^187+486x^188+1008x^189+312x^190+264x^191+494x^192+156x^193+102x^194+252x^195+96x^196+60x^197+128x^198+42x^199+24x^200+20x^201+6x^203+14x^204+8x^207+10x^210+4x^213+2x^216+4x^219 The gray image is a linear code over GF(3) with n=270, k=9 and d=165. This code was found by Heurico 1.16 in 9.21 seconds.