The generator matrix

 1  1  1  1  1
 0  X  0  0  X
 0  0  X  0 a^6*X
 0  0  0  X  X

generates a code of length 5 over F8[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+70x^16+420x^24+1505x^32+28672x^35+2100x^40

The gray image is a linear code over GF(8) with n=40, k=5 and d=16.
This code was found by Heurico 1.16 in 0.00865 seconds.