The generator matrix 1 0 0 0 1 1 1 1 2X 1 1 1 1 0 1 1 2X 1 1 2X 1 0 1 0 0 0 1 2X 2 1 2X+1 X+2 2X 2 1 2X 1 1 0 0 1 2 0 0 1 0 0 2 2X+1 2 2X X X+1 2X+2 X+1 2X+1 2X+1 0 X X+2 X+2 X 1 0 0 0 1 1 X+1 2X+2 2X 2X+1 2 2X 2X+2 1 2X X+1 2X+1 X+2 0 X+1 2X+2 2 0 0 0 0 2X 2X X 0 2X 2X 2X 2X X X 0 X X X 0 0 X generates a code of length 21 over Z3[X]/(X^2) who´s minimum homogenous weight is 33. Homogenous weight enumerator: w(x)=1x^0+168x^33+468x^34+288x^35+694x^36+1278x^37+708x^38+1340x^39+1884x^40+1308x^41+1906x^42+2724x^43+1422x^44+1722x^45+1872x^46+624x^47+688x^48+510x^49+24x^50+30x^51+12x^52+4x^54+6x^57+2x^60 The gray image is a linear code over GF(3) with n=63, k=9 and d=33. This code was found by Heurico 1.16 in 1.63 seconds.