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

generates a code of length 22 over F8[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+154x^144+217x^152+3584x^154+42x^160+35x^168+63x^176

The gray image is a linear code over GF(8) with n=176, k=4 and d=144.
This code was found by Heurico 1.16 in 0.00416 seconds.