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

generates a code of length 74 over Z3[X]/(X^2) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+52x^135+130x^138+248x^141+338x^144+442x^147+468x^150+286x^153+80x^156+36x^159+22x^162+26x^165+26x^168+8x^171+2x^174+10x^177+2x^180+4x^183+4x^186+2x^198

The gray image is a linear code over GF(3) with n=222, k=7 and d=135.
This code was found by Heurico 1.16 in 0.255 seconds.