The generator matrix

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

generates a code of length 15 over F8[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+651x^88+581x^96+966x^104+28672x^105+1386x^112+511x^120

The gray image is a linear code over GF(8) with n=120, k=5 and d=88.
This code was found by Heurico 1.16 in 10.6 seconds.