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

generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+58x^153+124x^156+252x^159+318x^162+474x^165+460x^168+266x^171+104x^174+24x^177+30x^180+10x^183+24x^186+12x^189+4x^192+14x^195+6x^198+2x^201+2x^210+2x^225

The gray image is a linear code over GF(3) with n=249, k=7 and d=153.
This code was found by Heurico 1.16 in 0.298 seconds.