The generator matrix
1 1 1 1 1 1 1
0 X 0 0 X X a*X
0 0 X 0 a^6*X a^5*X a*X
0 0 0 X X a^4*X a^4*X
generates a code of length 7 over F8[X]/(X^2) who´s minimum homogenous weight is 32.
Homogenous weight enumerator: w(x)=1x^0+245x^32+588x^40+1666x^48+28672x^49+1596x^56
The gray image is a linear code over GF(8) with n=56, k=5 and d=32.
This code was found by Heurico 1.16 in 0.0196 seconds.