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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+180x^114+24x^115+128x^117+132x^118+312x^121+164x^123+462x^124+54x^126+408x^127+120x^130+72x^132+38x^135+52x^141+16x^144+16x^150+6x^153+2x^168

The gray image is a linear code over GF(3) with n=186, k=7 and d=114.
This code was found by Heurico 1.16 in 43.1 seconds.