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

generates a code of length 49 over Z3[X]/(X^3) who�s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+34x^90+62x^93+54x^94+36x^96+216x^97+1458x^98+26x^99+216x^100+38x^102+12x^105+16x^108+8x^111+4x^114+4x^117+2x^141

The gray image is a linear code over GF(3) with n=441, k=7 and d=270.
This code was found by Heurico 1.16 in 0.0615 seconds.