The generator matrix

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

generates a code of length 44 over F8[X]/(X^2) who´s minimum homogenous weight is 296.

Homogenous weight enumerator: w(x)=1x^0+1400x^296+1680x^297+840x^298+1176x^299+4760x^304+3360x^305+1008x^306+784x^307+8603x^312+5712x^313+1736x^314+1624x^315+49x^320+14x^328+7x^344+14x^352

The gray image is a linear code over GF(8) with n=352, k=5 and d=296.
This code was found by Heurico 1.16 in 0.155 seconds.