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

generates a code of length 43 over F8[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+133x^272+616x^280+735x^288+3584x^294+644x^296+25088x^302+553x^304+525x^312+420x^320+266x^328+182x^336+21x^344

The gray image is a linear code over GF(8) with n=344, k=5 and d=272.
This code was found by Heurico 1.16 in 0.42 seconds.