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

generates a code of length 42 over F8[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+651x^272+686x^280+3584x^287+742x^288+25088x^295+602x^296+490x^304+378x^312+385x^320+126x^328+35x^336

The gray image is a linear code over GF(8) with n=336, k=5 and d=272.
This code was found by Heurico 1.16 in 39.8 seconds.