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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+48x^72+114x^75+106x^78+162x^80+106x^81+648x^83+4460x^84+648x^86+62x^87+56x^90+42x^93+38x^96+26x^99+26x^102+10x^105+6x^108+2x^120

The gray image is a linear code over GF(3) with n=378, k=8 and d=216.
This code was found by Heurico 1.16 in 0.232 seconds.