The generator matrix

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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+228x^76+234x^77+1884x^78+2448x^79+2436x^80+6652x^81+5394x^82+4404x^83+9028x^84+7410x^85+4902x^86+7446x^87+3498x^88+1074x^89+1432x^90+402x^91+60x^92+38x^93+48x^94+12x^95+6x^96+12x^97

The gray image is a linear code over GF(3) with n=378, k=10 and d=228.
This code was found by Heurico 1.16 in 4.6 seconds.