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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+130x^144+132x^147+254x^150+390x^153+486x^156+350x^159+264x^162+58x^165+24x^168+28x^171+16x^174+16x^177+18x^180+4x^183+4x^186+4x^189+6x^192+2x^207

The gray image is a linear code over GF(3) with n=234, k=7 and d=144.
This code was found by Heurico 1.16 in 6.97 seconds.