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

generates a code of length 70 over Z3[X]/(X^2) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+104x^123+198x^126+242x^129+214x^132+162x^134+228x^135+972x^137+176x^138+1944x^140+174x^141+1296x^143+154x^144+148x^147+162x^150+90x^153+104x^156+94x^159+50x^162+26x^165+8x^168+8x^171+4x^174+2x^201

The gray image is a linear code over GF(3) with n=210, k=8 and d=123.
This code was found by Heurico 1.16 in 1.45 seconds.