The generator matrix

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

generates a code of length 44 over F8[X]/(X^2) who´s minimum homogenous weight is 291.

Homogenous weight enumerator: w(x)=1x^0+4536x^291+224x^294+1512x^295+2800x^296+5544x^297+7168x^298+24304x^299+448x^301+3136x^302+9072x^303+9247x^304+11312x^305+9856x^306+38136x^307+3136x^309+10976x^310+21672x^311+16982x^312+18984x^313+15232x^314+47712x^315+56x^320+63x^328+28x^336+7x^344

The gray image is a linear code over GF(8) with n=352, k=6 and d=291.
This code was found by Heurico 1.16 in 60.8 seconds.