The generator matrix

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

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+62x^72+54x^73+162x^74+292x^75+180x^76+558x^77+1334x^78+990x^79+3402x^80+5094x^81+2394x^82+10260x^83+9690x^84+3222x^85+10278x^86+6718x^87+1602x^88+1296x^89+652x^90+306x^91+270x^92+74x^93+18x^95+76x^96+32x^99+22x^102+8x^105+2x^111

The gray image is a linear code over GF(3) with n=378, k=10 and d=216.
This code was found by Heurico 1.16 in 5.76 seconds.