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

generates a code of length 84 over Z3[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+98x^156+36x^158+140x^159+102x^161+40x^162+210x^164+114x^165+444x^167+106x^168+384x^170+18x^171+222x^173+58x^174+60x^176+38x^177+14x^180+34x^183+24x^186+6x^189+8x^192+10x^195+2x^198+8x^201+6x^204+2x^210+2x^228

The gray image is a linear code over GF(3) with n=252, k=7 and d=156.
This code was found by Heurico 1.16 in 0.538 seconds.