The generator matrix

 1  0  0  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 a^3*X  1  1  1  1 a*X
 0  1  0 a^7*X+1  a a^2 a^7*X+2 a^7*X+a^7  X a^7*X+a a^6 a^6*X+1 a^7*X+a^2 a^7*X+a^3 a^7 X+a^2 a^7*X+a^5  2 a^3 X+a^6 a^5*X+2 a^5*X+1 a^2*X+a^7 a^2*X+a a^6*X+a^3 a^5*X a*X+a a^2*X+a^3  1 2*X+a^6 a*X+a^6 2*X+1 a^6*X+2  1
 0  0  1 a^7*X+a^7  a a^6 a^7*X+a^5 a^7*X+2 a^7*X+a^3 a^7*X+a^2 X+a^6 a^3 a^6*X+a^7 a^6*X+a^2 X+a a^5*X+2 a^3*X+1 a*X+1 a^6*X+a^5 a*X+a^2 a^6*X+a^3 a*X+a^5 a^5*X a^5*X+a^7  2 a^5*X+a  X a^2*X+a^6 a^2*X+a a^6*X+2 a^5*X+a^5 a^7*X+a^6 2*X+a^7 a^6*X+a^5

generates a code of length 34 over F9[X]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+360x^256+2160x^257+13392x^258+24480x^259+272x^261+3888x^264+5760x^265+15120x^266+53568x^267+61200x^268+248x^270+29160x^272+31104x^273+23040x^274+41040x^275+113832x^276+112608x^277+80x^279+40x^288+48x^297+40x^306

The gray image is a linear code over GF(9) with n=306, k=6 and d=256.
This code was found by Heurico 1.16 in 31.8 seconds.