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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+106x^87+54x^88+62x^90+216x^91+1458x^92+216x^94+28x^96+8x^99+26x^105+10x^108+2x^132

The gray image is a linear code over GF(3) with n=414, k=7 and d=261.
This code was found by Heurico 1.16 in 41.4 seconds.