The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+168x^76+114x^77+444x^78+804x^79+858x^80+2140x^81+2994x^82+3924x^83+5010x^84+8676x^85+7212x^86+6760x^87+8988x^88+4938x^89+3396x^90+1314x^91+324x^92+342x^93+282x^94+108x^95+66x^96+90x^97+18x^98+50x^99+12x^100+8x^102+2x^105+2x^108+4x^111

The gray image is a linear code over GF(3) with n=387, k=10 and d=228.
This code was found by Heurico 1.16 in 5.91 seconds.