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

generates a code of length 23 over F8[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+203x^136+588x^144+735x^152+749x^160+28672x^161+805x^168+798x^176+217x^184

The gray image is a linear code over GF(8) with n=184, k=5 and d=136.
This code was found by Heurico 1.16 in 0.194 seconds.