The generator matrix

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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+62x^144+24x^145+24x^146+414x^147+168x^148+720x^149+1380x^150+552x^151+2280x^152+3300x^153+1080x^154+5760x^155+5748x^156+1116x^157+9222x^158+7698x^159+1554x^160+6984x^161+4814x^162+966x^163+2580x^164+1640x^165+282x^166+102x^167+248x^168+54x^169+24x^170+104x^171+36x^172+6x^173+24x^174+26x^177+18x^180+18x^183+8x^186+6x^189+4x^192+2x^198

The gray image is a linear code over GF(3) with n=711, k=10 and d=432.
This code was found by Heurico 1.16 in 12.5 seconds.