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  X  1  1  1  1  1  1  X  1  1  1  1  1  X  1
 0  X 2X  0 2X^2+X 2X X^2+2X X^2 2X^2+X 2X^2+X  0 2X 2X^2 X^2+2X 2X^2+X X^2+X  0 2X X^2 2X X^2 2X^2+2X 2X^2+X X^2 X^2+X  X X^2 2X^2+X X^2+2X 2X^2 X^2 X^2+2X 2X^2+2X 2X^2 2X 2X 2X^2 2X 2X^2+2X 2X^2+2X 2X^2  0
 0  0 X^2  0  0  0 2X^2  0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0 2X^2  0 2X^2  0  0 2X^2 X^2 X^2 2X^2 X^2  0 X^2 X^2 2X^2  0 2X^2 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2  0
 0  0  0 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 X^2 X^2 X^2  0 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2  0 X^2  0 2X^2 X^2  0 X^2  0 X^2 X^2 2X^2 X^2  0  0  0  0  0 X^2
 0  0  0  0 2X^2 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 X^2  0 X^2 2X^2 2X^2  0 X^2 X^2  0  0  0 2X^2 X^2 X^2 2X^2 2X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^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+138x^76+102x^78+324x^79+166x^81+1254x^82+1674x^84+2154x^85+196x^87+276x^88+12x^90+132x^91+66x^94+22x^96+30x^97+8x^99+4x^105+2x^117

The gray image is a linear code over GF(3) with n=378, k=8 and d=228.
This code was found by Heurico 1.16 in 0.177 seconds.