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 1 1 3 3 1 1 1 1 1 3 3 3 1 1 1 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 9 18 0 9 0 18 0 18 9 0 9 0 18 9 18 18 9 9 0 18 9 18 0 9 18 9 0 0 18 9 9 18 9 9 0 0 0 18 0 0 9 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 0 18 9 9 0 9 18 18 9 0 9 18 18 9 18 18 0 18 0 18 18 0 9 18 0 0 9 9 18 0 18 18 18 18 18 0 18 18 0 9 0 9 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 18 18 9 18 18 18 9 18 0 9 18 0 18 0 9 18 9 9 9 0 9 9 18 18 0 0 9 9 0 9 9 18 9 0 0 0 9 0 9 9 18 18 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 9 0 9 0 0 9 9 9 0 9 0 0 9 18 18 9 9 18 9 9 18 18 18 0 0 0 9 18 18 9 9 0 0 9 9 9 9 18 0 9 9 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 0 9 0 0 9 0 0 0 9 9 18 0 9 18 9 18 18 18 18 0 9 0 9 9 9 0 0 18 0 9 0 18 9 9 0 0 18 9 0 0 18 0 generates a code of length 67 over Z27 who´s minimum homogenous weight is 123. Homogenous weight enumerator: w(x)=1x^0+122x^123+6x^124+116x^126+60x^127+88x^129+240x^130+114x^132+480x^133+4374x^134+64x^135+480x^136+40x^138+192x^139+42x^141+24x^144+18x^147+28x^150+34x^153+14x^156+16x^159+4x^162+2x^165+2x^186 The gray image is a code over GF(3) with n=603, k=8 and d=369. This code was found by Heurico 1.16 in 56.1 seconds.