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

generates a code of length 76 over Z3[X]/(X^2) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+154x^141+186x^144+210x^147+516x^150+530x^153+276x^156+180x^159+32x^162+38x^168+30x^171+18x^177+2x^180+12x^186+2x^207

The gray image is a linear code over GF(3) with n=228, k=7 and d=141.
This code was found by Heurico 1.16 in 48 seconds.