The generator matrix

 1  0  0  1  1  1  1  1  1  1
 0  1  0  1  a a^2 a^6*X+a^3 a^6*X+a^4 a^5  X
 0  0  1 a^6  a a^4  1 a^5 a^3 a^3*X

generates a code of length 10 over F8[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+2072x^56+896x^57+3584x^63+22155x^64+8960x^65+100352x^70+25088x^71+80024x^72+18816x^73+196x^80

The gray image is a linear code over GF(8) with n=80, k=6 and d=56.
This code was found by Heurico 1.16 in 1.18 seconds.