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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+68x^84+78x^87+162x^88+1480x^90+324x^91+14x^93+18x^96+4x^99+26x^102+10x^105+2x^132

The gray image is a linear code over GF(3) with n=405, k=7 and d=252.
This code was found by Heurico 1.16 in 81.8 seconds.