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

generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+44x^144+84x^147+6x^148+118x^150+60x^151+84x^153+240x^154+102x^156+480x^157+64x^159+480x^160+50x^162+192x^163+28x^165+36x^168+22x^171+24x^174+24x^177+18x^180+12x^183+6x^186+6x^189+2x^192+2x^195+2x^222

The gray image is a linear code over GF(3) with n=237, k=7 and d=144.
This code was found by Heurico 1.16 in 0.234 seconds.