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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+108x^66+128x^69+264x^72+728x^75+728x^78+62x^81+56x^84+50x^87+20x^90+26x^93+12x^96+2x^99+2x^108

The gray image is a linear code over GF(3) with n=114, k=7 and d=66.
This code was found by Heurico 1.16 in 43.3 seconds.