The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 1 0 1 1 1 1 X 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 2X 2X 1 X 1 1 1 1 1 1 1 1 0 1 1 1 2X 1 2X 1 0 1 1 1 1 1 1 1 2X 1 0 X 1 1 1 X 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 0 1 2 2X+1 2 X 1 1 2X 0 1 2X+1 X+2 0 2 1 2X+1 X X 2X+2 1 2X+2 2X 1 1 X+2 1 X+1 X X X+1 2X+1 2X+1 X+1 2 1 X X 2X+2 1 X 1 2X+2 1 2X+1 1 2X 2 2X+2 1 X+2 1 X 1 1 2 X 1 0 0
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 2X X 0 2X X 2X 0 X X X 2X 0 2X 0 0 X X X 0 2X 2X X X X X X 2X X 2X 0 X 0 2X 2X X 0 2X 0 2X X X 0 X 0 0 0 X X X 2X 2X 2X 2X X 0 0 2X X X 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X 2X X X 0 X 0 0 0 X 2X 0 X 2X X 2X X X X 0 0 2X 0 2X 2X 0 2X X 2X 2X 2X 0 2X X 0 X 0 2X X 0 X 2X 0 0 0 X X 2X X 2X X X X 0 X 0 2X 0 X
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 X 0 0 X 2X 2X 2X 2X X X 2X X X 2X 2X X 2X X 0 0 X X 0 2X X X 2X X 0 0 X 2X X 0 X X 2X 2X X X 0 2X X X 0 2X X 2X 0 0 0 2X X 0 2X 0 0 0 X X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 0 0 X 0 0 2X 2X 2X 0 2X 2X X 2X X 2X 0 X 2X 2X X 0 X X 2X 0 0 X 2X 0 0 X X X 0 0 2X X 0 X X X 0 2X 0 X X 0 X 0 X X 2X X 2X 2X X 0 X 2X 2X
generates a code of length 80 over Z3[X]/(X^2) who´s minimum homogenous weight is 147.
Homogenous weight enumerator: w(x)=1x^0+206x^147+610x^150+788x^153+846x^156+1006x^159+1022x^162+968x^165+592x^168+334x^171+100x^174+28x^177+14x^180+14x^183+4x^186+6x^189+6x^192+10x^195+2x^198+2x^201+2x^207
The gray image is a linear code over GF(3) with n=240, k=8 and d=147.
This code was found by Heurico 1.16 in 0.978 seconds.