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

generates a code of length 45 over F8[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+238x^272+1260x^280+2450x^288+3115x^296+3584x^301+4214x^304+50176x^309+4753x^312+175616x^317+5719x^320+5215x^328+3556x^336+1743x^344+462x^352+42x^360

The gray image is a linear code over GF(8) with n=360, k=6 and d=272.
This code was found by Heurico 1.16 in 26.3 seconds.