The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+48x^75+54x^77+206x^78+72x^79+444x^80+662x^81+1152x^82+2052x^83+1790x^84+6048x^85+5256x^86+3920x^87+12096x^88+6978x^89+4220x^90+8136x^91+3780x^92+1118x^93+162x^94+360x^95+238x^96+36x^97+30x^98+116x^99+26x^102+26x^105+14x^108+6x^111+2x^114

The gray image is a linear code over GF(3) with n=396, k=10 and d=225.
This code was found by Heurico 1.16 in 6 seconds.