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.