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

generates a code of length 30 over F8[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+735x^176+2142x^184+3164x^192+4410x^200+28672x^203+6209x^208+200704x^211+7434x^216+5607x^224+2590x^232+476x^240

The gray image is a linear code over GF(8) with n=240, k=6 and d=176.
This code was found by Heurico 1.16 in 16.2 seconds.