The generator matrix

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

generates a code of length 44 over F8[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+217x^280+56x^283+56x^287+1281x^288+3248x^290+1568x^291+1176x^295+9170x^296+10416x^298+4368x^299+8232x^303+39060x^304+33936x^306+11424x^307+19208x^311+67767x^312+38416x^314+11256x^315+441x^320+392x^328+308x^336+126x^344+21x^352

The gray image is a linear code over GF(8) with n=352, k=6 and d=280.
This code was found by Heurico 1.16 in 10.1 seconds.