The generator matrix

 1  0  1  1  1  1  1  X 2X  1  1  1  1 2X^2  1  1  X  1  1  1  1  1  1  1 2X^2+2X  1  1 2X^2+X  1  1  1  1  0  1  1 X^2+X  1  1  1 X^2  1  1  1  1  0  1 2X^2  1  1  1  1 X^2+2X  1  1  1  1  1  1  1  1  1  1 2X^2+X  1  1  1  1  1  1  1  X  1  1  1
 0  1  1  2 2X^2 2X+1  2  1  1  2 2X^2+2X+1 2X^2+X X+1  1 2X^2 X+2  1 X^2+2X X^2+2X+2 2X^2+X+1 2X^2 X+2 X^2+X+1 2X^2+2X  1 2X^2+1 2X^2+X+2  1  X X+2 2X^2+2X+1 2X^2+X+1  1 X^2+2X X^2+X+2  1 2X^2+2 X^2+X+2  1  1 X+1 2X^2  X X+2  1 X^2+2X  1 X^2+2X+1 X+1 2X^2+X+1 X^2+X  1  X 2X^2+2X+2 X^2+2X X^2+2  X 2X^2+2X+1 X+2  2 2X^2 X^2+2X+1  1 X^2+2 2X+1 X^2+2X 2X+1 X^2+2X+1 X^2+X 2X^2+2X  1 X^2+X X^2+2X+2 2X^2
 0  0 2X  0 2X^2  0  0 X^2  0 2X^2 2X^2 X^2 X^2 X^2+X  X 2X^2+2X 2X 2X X^2+X X^2+X 2X^2+X 2X^2+X 2X 2X X^2+2X X^2+X X^2+X 2X^2+X 2X^2+2X X^2+2X  X 2X X^2+X 2X^2+X X^2+2X 2X 2X^2+X  0 2X X^2+2X X^2  X  X X^2+X 2X 2X^2  0 X^2+2X 2X^2 X^2+2X  X X^2 2X^2+2X 2X^2 X^2+2X 2X 2X^2+2X  X X^2+2X  X X^2 X^2+X 2X X^2+X 2X^2 X^2+2X  X 2X^2+2X 2X^2  X  X X^2 2X^2+X X^2+X
 0  0  0  X 2X^2+X X^2+X X^2  X X^2+2X X^2+2X 2X^2+2X 2X 2X^2 X^2+2X X^2 X^2+X 2X 2X^2+X 2X^2+2X X^2 2X^2+2X 2X^2  X 2X^2  0 2X  X 2X^2 X^2+2X X^2 2X^2+X 2X^2+2X 2X^2+X 2X 2X^2+2X  X 2X^2 X^2 X^2+X 2X^2+2X X^2 X^2+X 2X^2 2X X^2 2X^2+2X  X 2X X^2+X  0 X^2+X 2X^2 2X X^2+2X 2X X^2  0 2X  X 2X^2+X X^2+X  X 2X^2+X 2X^2+X  X 2X^2 X^2 2X^2 2X^2+X  X 2X^2+X 2X^2  X X^2+2X

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+108x^137+168x^138+468x^139+882x^140+1786x^141+2208x^142+2460x^143+3026x^144+4368x^145+4704x^146+5096x^147+6942x^148+5580x^149+5760x^150+5358x^151+3528x^152+2682x^153+1614x^154+858x^155+488x^156+222x^157+192x^158+64x^159+114x^160+90x^161+72x^162+66x^163+36x^164+38x^165+18x^166+24x^167+14x^168+6x^169+6x^170+2x^177

The gray image is a linear code over GF(3) with n=666, k=10 and d=411.
This code was found by Heurico 1.16 in 10.9 seconds.