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  X  1  1  1  1  1  X  1  1  1  X  1  1  1  1  1  1  1  X  1  X  1  1  1  X  X  1  1  X  1  1  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2  0 2X^2 X^2  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2  0 X^2  0 2X^2 X^2 X^2  0 2X^2 X^2 X^2  0 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0 2X^2 X^2 X^2  0  0  0  0 2X^2 2X^2 X^2 X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0 X^2 X^2 2X^2 X^2 2X^2  0 X^2 2X^2  0 2X^2  0  0 X^2  0  0 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 X^2  0 2X^2  0 X^2 2X^2 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 2X^2  0 X^2 X^2 2X^2  0  0 2X^2  0  0 2X^2 2X^2 X^2  0  0
 0  0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 X^2  0 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 2X^2 2X^2  0  0 2X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2 X^2  0 X^2  0  0 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2  0 2X^2 X^2  0  0 X^2  0 X^2  0 X^2 2X^2  0  0 X^2 X^2 X^2 X^2 2X^2  0 X^2 2X^2 2X^2  0
 0  0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0 2X^2 X^2 2X^2 X^2  0 X^2 2X^2  0 X^2  0  0 2X^2 2X^2 X^2 2X^2  0  0  0  0 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2 X^2 X^2 X^2  0  0  0 2X^2 2X^2 X^2  0 2X^2 X^2  0  0 X^2  0  0  0 2X^2  0 X^2 X^2  0 X^2  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0  0 2X^2 2X^2  0 2X^2 X^2 2X^2  0  0 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2  0 2X^2  0  0  0  0  0 2X^2  0  0 2X^2 X^2 X^2  0 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 2X^2  0  0 2X^2 2X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2  0  0 X^2  0 2X^2 2X^2 2X^2  0 X^2 X^2  0  0 2X^2  0 X^2 2X^2  0 2X^2  0 X^2  0 X^2 2X^2 2X^2 2X^2  0 X^2 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2 X^2  0 X^2  0  0 2X^2  0  0 2X^2 2X^2  0 2X^2 2X^2 X^2 2X^2  0 2X^2  0  0 2X^2

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+60x^141+142x^144+216x^147+316x^150+522x^153+874x^156+1486x^159+13122x^160+1298x^162+846x^165+290x^168+136x^171+106x^174+66x^177+70x^180+54x^183+42x^186+14x^189+10x^192+8x^195+2x^198+2x^216

The gray image is a linear code over GF(3) with n=720, k=9 and d=423.
This code was found by Heurico 1.16 in 4.48 seconds.