The generator matrix

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

generates a code of length 27 over F8[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+3969x^176+7392x^177+8400x^178+4928x^182+23338x^184+24640x^185+16800x^186+7168x^189+34496x^190+55545x^192+46816x^193+28560x^194+77x^208+14x^216

The gray image is a linear code over GF(8) with n=216, k=6 and d=176.
This code was found by Heurico 1.16 in 4.09 seconds.