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 3 1 1 3 1 1 1 3 3 1 1 1 1 3 1 3 9 1 3 1 1 1 0 9 0 0 0 0 0 0 0 0 9 18 18 9 9 9 0 18 9 18 9 0 9 0 18 9 0 18 9 18 18 18 9 9 0 9 18 18 0 0 0 9 18 9 9 9 0 9 9 0 18 18 0 9 0 18 18 18 9 9 0 0 9 0 0 9 0 0 0 0 9 0 0 0 0 9 18 18 18 0 0 18 9 18 9 0 9 9 0 18 18 0 9 9 18 0 9 0 18 18 18 9 0 18 18 18 9 9 18 18 18 18 0 18 0 0 18 9 9 0 18 18 9 0 0 18 9 18 18 9 18 0 9 0 0 0 0 0 0 9 0 0 9 18 0 18 0 0 18 9 9 18 0 9 0 18 0 18 18 0 18 0 9 18 18 9 9 9 18 0 18 0 18 9 0 18 9 18 18 9 9 0 0 18 9 18 0 18 18 0 0 18 0 0 18 18 0 9 9 9 9 9 18 0 0 0 0 0 9 0 18 18 9 0 18 18 18 0 18 18 0 18 9 0 18 18 0 9 18 0 18 9 0 9 0 9 0 18 18 0 0 18 18 9 0 9 18 9 0 9 0 18 18 18 9 0 9 9 9 18 9 0 18 9 9 9 0 18 0 9 18 0 0 0 0 0 0 9 18 18 18 18 18 18 9 18 9 9 18 9 18 18 18 18 0 18 0 9 0 0 18 9 18 0 18 9 9 0 9 0 0 9 0 9 18 9 18 0 9 0 9 9 9 9 18 0 0 0 0 18 18 9 0 0 0 0 9 18 9 18 generates a code of length 68 over Z27 who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+44x^123+154x^126+226x^129+318x^132+1458x^134+496x^135+2916x^137+412x^138+310x^141+90x^144+36x^147+16x^150+24x^153+20x^156+12x^159+16x^162+8x^165+2x^168+2x^180 The gray image is a code over GF(3) with n=612, k=8 and d=369. This code was found by Heurico 1.16 in 0.498 seconds.