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  0  0  0  0  X 2X 2X  0  0  X  X  X  X  X  X  X  0 2X  0 2X  0 2X  0  X  X 2X  0  X  X  0  X 2X  0 2X 2X 2X 2X 2X  X  X 2X 2X  0  X 2X  0  0
 0  0  X  0  0  X 2X  0 2X  0  X  X 2X 2X  0  X  0  X  X  X  X  0  0 2X 2X  X 2X  0 2X  X 2X  X  X  0  0 2X  0 2X  X  0 2X  X  X  X 2X  0 2X 2X  0
 0  0  0  X  0 2X 2X  X  0  X  X  0  0  X 2X  X  X 2X 2X  0  0 2X 2X 2X 2X 2X  0  0  X  X  X  X 2X  0  0  0 2X 2X  X  X 2X  X 2X 2X 2X  X  0  X 2X
 0  0  0  0  X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  X  0  0 2X 2X  X 2X  X 2X 2X  0  0  0  X 2X  0  X 2X  0  X  0  X  0  X  X 2X  X  0  X  X  X  0

generates a code of length 49 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+34x^90+62x^93+54x^94+36x^96+216x^97+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=147, k=6 and d=90.
This code was found by Heurico 1.16 in 0.0226 seconds.