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  3  1  3  1  1  1  1  1  3  1  1  1  1  1  1  1  1  3  1  1  3  1  3  3  1  3  3
 0  3  0  0  0  0  0  0  0  0  3  6  6  3  3  3  0  6  3  6  3  0  3  0  6  3  0  6  3  6  6  6  3  3  3  0  6  6  0  0  0  3  6  3  0  6  3  6  3  6  6  0  3  0  3  0  6  3  3  0  0  6  0  6  6  6  6  3  0  0  0  3  3  6  0  6  3  0
 0  0  3  0  0  0  0  3  6  6  6  0  0  6  3  6  3  0  3  3  0  6  6  0  3  3  6  0  3  0  6  6  6  3  6  0  6  6  3  3  6  6  6  6  0  0  6  6  0  3  0  3  3  3  3  6  6  0  3  3  0  0  3  0  6  0  3  3  3  3  3  6  0  0  6  6  3  3
 0  0  0  3  0  0  3  6  0  6  0  0  6  3  3  6  0  3  0  6  0  6  6  0  6  0  3  6  6  3  3  3  6  0  0  6  6  3  6  0  3  6  6  3  3  6  3  6  6  0  3  6  6  3  6  3  0  6  3  3  3  0  0  6  6  0  3  0  0  0  3  0  3  3  0  0  0  6
 0  0  0  0  3  0  6  6  3  0  6  6  6  0  6  6  0  6  3  0  6  6  0  3  6  0  6  3  0  3  0  3  0  6  0  6  0  6  3  6  0  3  6  3  6  0  6  6  0  3  3  6  0  6  6  0  0  6  0  3  3  3  6  0  6  3  3  6  3  3  0  3  0  3  0  6  6  0
 0  0  0  0  0  3  6  6  6  6  6  6  3  6  3  3  6  3  6  6  6  6  0  6  0  3  0  0  6  3  6  0  6  3  0  3  3  0  3  0  0  3  6  3  3  3  3  0  3  3  6  3  3  6  6  3  3  6  0  0  3  0  6  6  3  6  0  6  6  3  6  0  3  0  0  0  0  3

generates a code of length 78 over Z9 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 code over GF(3) with n=234, k=7 and d=144.
This code was found by Heurico 1.16 in 6.81 seconds.