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 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 X 0 1 1 1 1 X 1 X 0 1 0 1 0 1 1 0 1 1 0 X 2X 0 2X^2+X 2X X^2 2X^2+X X^2+2X 0 2X^2+X 2X 2X^2 X^2+X 2X^2+2X 2X 2X^2+X 0 2X^2 2X X 2X^2+2X X^2+2X 2X^2+X 0 2X^2+X X^2 X 0 X^2 X X X 2X X^2+2X X^2 X^2+2X 2X^2 X^2+2X 2X 2X^2 2X^2+2X X 2X X 2X^2+X 2X^2+X 2X^2 0 2X^2+X 2X 0 0 2X X 2X 2X^2+2X 2X^2 2X^2 2X^2+X X 2X X 2X^2+X X X^2+X X 2X^2+X X^2+2X X 2X 0 0 0 X^2 0 0 0 0 0 2X^2 0 2X^2 2X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 2X^2 0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 0 2X^2 2X^2 X^2 0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 0 0 X^2 0 2X^2 X^2 0 0 0 0 0 0 2X^2 X^2 0 2X^2 2X^2 X^2 2X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 2X^2 0 0 X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 X^2 2X^2 0 X^2 X^2 0 0 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 0 0 2X^2 0 2X^2 0 X^2 2X^2 0 0 0 2X^2 2X^2 2X^2 2X^2 0 0 0 2X^2 X^2 X^2 2X^2 0 0 2X^2 0 0 0 X^2 X^2 X^2 0 2X^2 2X^2 2X^2 0 0 0 0 2X^2 0 0 X^2 0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 0 X^2 0 2X^2 0 2X^2 X^2 2X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 2X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 2X^2 2X^2 X^2 2X^2 0 2X^2 0 0 X^2 0 0 2X^2 X^2 0 0 X^2 2X^2 X^2 2X^2 X^2 0 0 0 2X^2 2X^2 2X^2 X^2 2X^2 0 0 0 0 0 0 X^2 0 0 2X^2 2X^2 0 2X^2 X^2 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 0 2X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 0 2X^2 X^2 0 0 0 0 X^2 0 2X^2 X^2 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 0 generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 132. Homogenous weight enumerator: w(x)=1x^0+296x^132+18x^134+602x^135+180x^137+840x^138+1692x^140+1058x^141+5328x^143+1136x^144+5328x^146+984x^147+576x^149+832x^150+468x^153+174x^156+106x^159+28x^162+22x^168+4x^171+8x^177+2x^189 The gray image is a linear code over GF(3) with n=648, k=9 and d=396. This code was found by Heurico 1.16 in 30.7 seconds.