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

generates a code of length 42 over F8[X]/(X^2) who´s minimum homogenous weight is 277.

Homogenous weight enumerator: w(x)=1x^0+3584x^277+511x^280+1344x^281+3640x^282+5264x^283+9520x^284+19320x^285+448x^287+4788x^288+8064x^289+12432x^290+11872x^291+13216x^292+29008x^293+3136x^295+16534x^296+19264x^297+23352x^298+18704x^299+20272x^300+37688x^301+77x^304+56x^312+42x^320+7x^328

The gray image is a linear code over GF(8) with n=336, k=6 and d=277.
This code was found by Heurico 1.16 in 9.13 seconds.