The generator matrix

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

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+136x^147+84x^148+132x^149+514x^150+828x^151+342x^152+1802x^153+2772x^154+672x^155+3850x^156+5538x^157+1446x^158+7382x^159+8154x^160+1578x^161+7356x^162+7200x^163+1080x^164+3446x^165+2784x^166+468x^167+686x^168+252x^169+78x^170+188x^171+72x^172+30x^173+74x^174+18x^175+6x^176+18x^177+20x^180+12x^183+2x^186+18x^189+4x^192+2x^195+2x^198+2x^210

The gray image is a linear code over GF(3) with n=720, k=10 and d=441.
This code was found by Heurico 1.16 in 13 seconds.