The generator matrix 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 2X 1 1 X 0 1 0 1 0 1 0 2 1 2 1 0 2X+1 1 2 2X X 1 0 X+2 1 X 0 0 0 1 2 1 2 1 0 2 X+2 2X 1 2X+2 2 2X+1 X X+2 X 2X+1 1 0 0 0 0 2X 0 2X 0 2X 2X 2X 2X X 0 X 0 2X 2X 2X 2X 2X 2X 0 0 0 0 2X X X 2X 2X 2X 2X 0 0 2X X 0 X X 2X 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+42x^33+42x^34+120x^35+498x^36+192x^37+270x^38+624x^39+414x^40+384x^41+1174x^42+426x^43+402x^44+904x^45+330x^46+252x^47+364x^48+54x^49+30x^50+26x^51+10x^54+2x^57 The gray image is a linear code over GF(3) with n=63, k=8 and d=33. This code was found by Heurico 1.16 in 0.13 seconds.