The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+294x^79+606x^80+820x^81+1428x^82+2250x^83+3250x^84+3600x^85+5508x^86+7234x^87+6396x^88+7998x^89+7842x^90+4560x^91+3300x^92+1898x^93+936x^94+558x^95+56x^96+222x^97+162x^98+40x^99+60x^100+30x^101

The gray image is a linear code over GF(3) with n=396, k=10 and d=237.
This code was found by Heurico 1.16 in 10.6 seconds.