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

generates a code of length 75 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+94x^138+6x^139+124x^141+66x^142+94x^144+192x^145+80x^147+342x^148+66x^150+474x^151+48x^153+294x^154+64x^156+84x^157+48x^159+20x^162+16x^165+24x^168+26x^171+6x^174+2x^177+10x^183+4x^186+2x^204

The gray image is a linear code over GF(3) with n=225, k=7 and d=138.
This code was found by Heurico 1.16 in 0.263 seconds.