The generator matrix

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

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+77x^296+231x^304+3584x^308+140x^312+28x^320+7x^328+7x^336+21x^352

The gray image is a linear code over GF(8) with n=352, k=4 and d=296.
This code was found by Heurico 1.16 in 0.0158 seconds.