The generator matrix

 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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0  X  0  0  0  X  X  X a*X  0  X a*X a*X a*X a*X  X a*X a^5*X  0  0  X a^6*X a^5*X a^3*X a^2*X a^3*X  0 a^3*X a^2*X a^2*X a^5*X a^5*X  X a^5*X a^3*X  0 a^3*X a^6*X a^5*X  X a^4*X  X a*X  0
 0  0  X  0  0 a^6*X a^5*X a^4*X a^4*X  X a^3*X a^6*X  0  X a^5*X a^2*X a*X a^6*X a^2*X a*X  0 a^4*X  X  0 a^4*X a^2*X a^2*X a^6*X a^2*X  0 a^6*X a^5*X  X a^6*X a^5*X a^5*X a^4*X  0  0 a*X a^5*X a^3*X a^5*X  0
 0  0  0  X  0  X a^5*X a*X a^3*X a^2*X a^6*X  0 a^5*X  X a*X a^4*X a^4*X a^4*X  X a^4*X a*X a*X a^4*X a^4*X a^3*X  0 a^2*X  0 a^4*X  X  0  X a*X a^3*X a^5*X  X a^6*X a^3*X a^4*X a^5*X  0 a^2*X a*X  0
 0  0  0  0  X a^6*X a^3*X a*X a^5*X a*X a^2*X a^2*X a^3*X  0 a*X  0 a^2*X a^4*X a^4*X  X a^3*X a^5*X a^6*X a^3*X  X a*X a^6*X a^2*X  X a^2*X a^5*X a*X a*X a^6*X a*X a^5*X a^6*X a^2*X a^2*X a^2*X a^3*X a*X a^3*X  0

generates a code of length 44 over F8[X]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+245x^264+1190x^272+2254x^280+2968x^288+4102x^296+28672x^301+4676x^304+200704x^309+5173x^312+5600x^320+4095x^328+1820x^336+595x^344+49x^352

The gray image is a linear code over GF(8) with n=352, k=6 and d=264.
This code was found by Heurico 1.16 in 25.5 seconds.