The generator matrix
1 1 1 1 1
0 X 0 X a*X
0 0 X a^6*X a^2*X
generates a code of length 5 over F8[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+70x^24+175x^32+3584x^35+266x^40
The gray image is a linear code over GF(8) with n=40, k=4 and d=24.
This code was found by Heurico 1.16 in 0.000329 seconds.