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 X 1 1 1 1 X 1 X 1 1 X X 1 X 1 1 1 1 X 1 1 1 X 1 1 1 X 1 X 1 X X 1 X 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 0 X 0 0 0 0 0 0 0 X 0 0 X X X 0 2X 2X X 0 2X 2X 0 2X X 0 2X 0 X X 0 2X X X X X 2X 0 0 X X 0 2X 0 2X X 0 2X X X 2X 2X 2X 0 X X X X X 2X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 2X 0 X 2X X X 2X 2X 0 X 2X 2X 2X X X 2X 2X X X 2X 2X 0 0 0 0 X 0 X 0 X X 2X 0 X X 2X 0 0 X 0 0 0 2X X 0 2X 2X 2X 0 X 2X 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 2X 0 2X 0 X 2X 2X 0 X 2X X 0 X 0 2X 2X 2X 2X X 2X 0 X X X X X X 2X 0 0 0 2X X 0 X 0 2X X 0 X 2X X X X X 0 X X X 2X X 0 X 2X 0 0 X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 2X X 2X 2X X 2X X 2X 2X 0 0 2X 2X 2X 2X X 2X X 0 0 2X 2X 0 2X 0 2X 2X 0 X 2X 0 X 2X 2X 2X 0 0 2X 2X X X 2X X 0 0 0 X X 0 0 2X 2X 2X X 2X 0 X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 2X 2X 2X X 0 0 2X 2X 2X X X X X 0 2X 0 2X X 2X 2X 2X 0 X 2X X 2X X 0 0 0 2X 0 2X 0 X 2X X 2X X X X X 2X 0 2X X X 2X 2X X 0 0 X 2X 0 X 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 2X 2X X 0 2X 2X 0 2X X 0 X 2X X 2X 2X 0 X X X X X 2X 0 X X 2X 2X 0 0 0 0 0 0 X X 0 0 0 0 0 0 X 2X X 2X X 2X 2X 0 X 2X 2X 2X 0 2X 2X 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 2X 2X 0 X 2X 0 X X 0 X 0 2X 2X 0 X X 2X 0 X 0 2X X X X X X X X X X 2X 2X 2X X X 0 2X 2X 2X X X 2X X X 2X 2X 2X 0 X X 2X 0 X 0 0 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X X 0 X 0 X X 0 2X X 2X 2X 0 2X X 0 X 0 2X 2X X X 2X 2X 0 2X X 2X X X 0 0 2X X 0 0 0 0 X 0 2X X 2X 2X 2X X X 2X 2X 0 2X 2X 2X 0 2X X X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 105. Homogenous weight enumerator: w(x)=1x^0+26x^105+88x^108+178x^111+234x^114+300x^117+432x^120+500x^123+546x^126+636x^129+646x^132+636x^135+604x^138+526x^141+410x^144+290x^147+240x^150+134x^153+62x^156+38x^159+18x^162+48x^163+12x^165+342x^166+4x^168+990x^169+2610x^172+26x^174+5598x^175+118x^177+8010x^178+204x^180+9162x^181+386x^183+7002x^184+440x^186+4122x^187+508x^189+1302x^190+726x^192+180x^193+964x^195+1086x^198+1314x^201+1332x^204+1298x^207+1236x^210+1086x^213+886x^216+580x^219+400x^222+250x^225+146x^228+78x^231+32x^234+14x^237+8x^240+2x^243+2x^249 The gray image is a linear code over GF(3) with n=270, k=10 and d=105. This code was found by Heurico 1.16 in 99.7 seconds.