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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+292x^144+126x^147+252x^150+582x^153+468x^156+180x^159+184x^162+56x^171+40x^180+4x^189+2x^207

The gray image is a linear code over GF(3) with n=231, k=7 and d=144.
This code was found by Heurico 1.16 in 14.9 seconds.