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

generates a code of length 31 over F8[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+217x^176+973x^184+2338x^192+3227x^200+3584x^203+4571x^208+50176x^211+6097x^216+175616x^219+6993x^224+5369x^232+2520x^240+462x^248

The gray image is a linear code over GF(8) with n=248, k=6 and d=176.
This code was found by Heurico 1.16 in 16.7 seconds.