The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1
 0  1  1  a a^6*X+a^2 a^3 a^6*X+a^4 a^5 a^6*X+a^6  a a^6*X+a^2  0 a^6*X+1 a^5  a  1  0 a^3 a^6*X+a^4 a^6*X+a^2 a^5  1  X
 0  0 a^6*X  0  X  X a^3*X  X a^2*X a^3*X a^6*X a^2*X a^2*X  0 a^2*X a^6*X a^4*X a^4*X a^4*X  0  X a^3*X a^6*X
 0  0  0  X a^6*X a^5*X a^3*X a^2*X a^5*X a^6*X a^6*X a^4*X a*X a^2*X  0 a^2*X a^3*X a*X a^2*X a^4*X  X  0 a*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+112x^136+224x^140+168x^141+672x^144+1344x^147+4704x^148+2184x^149+735x^152+3584x^154+18816x^155+32928x^156+9464x^157+777x^160+25088x^162+65856x^163+76832x^164+16856x^165+798x^168+854x^176+147x^184

The gray image is a linear code over GF(8) with n=184, k=6 and d=136.
This code was found by Heurico 1.16 in 4.49 seconds.