The generator matrix

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

generates a code of length 42 over F8[X]/(X^2) who´s minimum homogenous weight is 282.

Homogenous weight enumerator: w(x)=1x^0+2016x^282+2520x^284+273x^288+6720x^290+3024x^292+168x^296+12768x^298+5208x^300+42x^304+28x^336

The gray image is a linear code over GF(8) with n=336, k=5 and d=282.
This code was found by Heurico 1.16 in 16.3 seconds.