The generator matrix 1 0 0 0 1 1 1 2X^2 1 1 1 1 1 2X 1 1 1 X 1 2X^2+X 2X^2+2X 1 1 X^2+X 1 1 1 1 2X^2+X 1 1 2X 1 2X^2+2X 2X^2+X 1 1 1 1 X^2 1 X^2+X 1 1 1 2X^2+2X 1 2X^2+X 1 1 1 1 1 1 1 X^2+2X 1 1 2X^2+2X 1 1 1 2X^2+2X 1 1 0 X^2 1 1 1 X^2+X 1 0 1 0 0 2X^2 1 X^2+1 1 X X^2+X 2X^2+2X+2 X^2+2 X^2+X+1 1 X^2+2 2X^2+2X+1 2X+2 1 X+1 1 X^2 2 2X^2 1 X^2+2X+1 2 2X^2+X 2X^2+2X+2 1 X^2+2X X+1 1 2X^2+X+1 1 0 X^2+2X+2 2X 2X^2 2X^2+1 1 2X^2+1 1 2X^2+X+2 2X^2+1 X^2+2X+1 1 2X+1 1 X^2+2X+1 1 2X^2+2X 2X+2 X^2+X 2X+1 2 1 X^2 2X^2+X 1 2 2X^2+2X+2 0 1 2X 2X+1 1 1 X 2X^2+2X+2 2X 1 0 0 0 1 0 2X^2+2X+1 2X+1 2X^2+X+2 2X^2+2X+1 X+1 X+2 2X^2 2X^2+X+1 2X^2+X+2 2X+2 X^2+2 X^2+2X+1 X^2+2X+2 2X^2+2 X^2+X 2X^2 1 1 2X^2+2X X^2+X+1 0 X^2+2X X X 2X^2+2X+1 2X+2 X^2+2X 2X^2+2X 2X^2+2 2X^2+2 1 2 2 2X^2+X+1 2X X^2+2X+1 1 2X^2+2X X^2+X+1 X^2 X^2+2X+2 X+2 1 2 X^2+2 X^2+X+2 2X^2+X 0 2X^2+2X+2 X^2+2X+1 0 X^2+2X+1 2X^2+1 2X^2+2 2X X+1 X+2 2X^2 X+1 2X^2+2X+1 2X+1 X^2+2X+2 2X+1 X^2+2X+1 X^2+X+2 2X^2+2X+2 2X^2 2X 0 0 0 1 2X^2+2X+2 X^2 X^2+2X+2 X^2+2X+2 1 X^2+X 2X^2+1 2X^2+2X 2X^2+2X+1 0 2X^2 2X^2+2 X^2+X+2 2X^2+2X+2 X^2+2 2X^2+2 2 X^2+2X+1 2X^2+X+2 2X^2+2X+1 2X 2 X^2+2X+1 X X 2X+2 1 X^2+1 X^2+2X 2X^2+X+1 2X^2+1 X^2+X+1 X^2+2X+1 0 2X^2+X 2X^2+X+2 2X^2+X+1 1 X^2+2X+2 X+1 X^2+X 2X^2 X^2+2X+2 2X^2+2X+1 X^2+2 X^2+1 2X^2 X X^2+1 2X X+2 X+1 X 2X+2 X^2+2X+2 X^2+2 2X^2+2X 2X^2+2X+1 X^2+X X^2+2X+2 2X+1 X+2 1 2X^2 X^2+X+1 2X^2+2X X^2+X+2 2X^2 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+384x^132+1308x^133+3834x^134+5542x^135+9108x^136+14244x^137+15618x^138+22854x^139+31176x^140+33390x^141+42948x^142+51888x^143+47720x^144+52440x^145+53622x^146+41354x^147+35832x^148+29616x^149+16062x^150+11010x^151+6366x^152+2682x^153+1302x^154+672x^155+202x^156+42x^157+48x^158+84x^159+48x^160+12x^161+14x^162+6x^163+6x^164+6x^166 The gray image is a linear code over GF(3) with n=648, k=12 and d=396. This code was found by Heurico 1.16 in 601 seconds.