The generator matrix

 1  0  1  1  1
 0  1 a^6*X+1  a a^6*X+a^2

generates a code of length 5 over F8[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+280x^28+35x^32+1792x^35+1960x^36+28x^40

The gray image is a linear code over GF(8) with n=40, k=4 and d=28.
This code was found by Heurico 1.16 in 0.00018 seconds.