The generator matrix

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

generates a code of length 28 over F8[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+616x^176+707x^184+3584x^189+798x^192+25088x^197+686x^200+658x^208+511x^216+119x^224

The gray image is a linear code over GF(8) with n=224, k=5 and d=176.
This code was found by Heurico 1.16 in 7.11 seconds.