The generator matrix

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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+654x^74+1626x^75+4494x^76+6678x^77+12044x^78+17304x^79+26172x^80+38984x^81+46428x^82+60462x^83+74420x^84+67806x^85+63762x^86+50972x^87+29310x^88+17040x^89+8086x^90+4182x^91+588x^92+172x^93+60x^94+84x^95+62x^96+24x^97+6x^98+14x^99+6x^100

The gray image is a linear code over GF(3) with n=378, k=12 and d=222.
This code was found by Heurico 1.16 in 313 seconds.