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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+340x^141+792x^144+972x^146+1080x^147+1944x^149+892x^150+198x^153+96x^156+136x^159+78x^162+30x^165+2x^216

The gray image is a linear code over GF(3) with n=666, k=8 and d=423.
This code was found by Heurico 1.16 in 0.451 seconds.