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

generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+90x^48+132x^51+84x^54+486x^56+90x^57+972x^59+84x^60+82x^63+80x^66+54x^69+22x^72+8x^75+2x^84

The gray image is a linear code over GF(3) with n=87, k=7 and d=48.
This code was found by Heurico 1.16 in 0.153 seconds.