The generator matrix

 1  0  0  0  1  1  1  6  1  1  4  0  1  1  6  1  1  2  1  2  4  6  4  4  1  1  0  4  1  1  1  1  1  1  2  4  1  1  6  1  4  1  1  6  1  1  1  2  0  4  1  1  1  1  1  1
 0  1  0  0  2  1  3  1  2  2  1  1  1  5  0  4  7  6  5  6  1  1  1  4  3  7  6  1  6  6  2  2  3  6  1  1  5  4  1  7  1  4  0  1  7  6  3  1  1  2  2  4  4  0  0  0
 0  0  1  0  3  1  6  3  0  1  2  1  1  0  1  2  4  1  1  4  2  5  1  1  4  5  1  0  0  2  5  1  7  7  0  5  1  0  6  4  7  3  2  3  1  0  7  0  5  1  6  3  5  1  0  0
 0  0  0  1  1  6  3  3  1  0  3  2  3  0  3  3  7  1  1  1  0  4  3  2  0  6  4  5  4  3  2  7  7  4  5  1  2  0  7  4  7  2  6  0  7  5  6  6  3  1  2  1  5  5  0  0
 0  0  0  0  4  0  0  0  0  4  4  4  0  0  4  4  4  0  4  0  0  4  4  4  4  0  0  0  4  4  4  4  4  0  0  0  0  0  0  0  0  0  0  4  0  4  4  4  4  4  0  0  4  0  0  0
 0  0  0  0  0  4  0  0  0  0  0  0  4  0  4  4  0  4  4  0  4  4  4  0  4  4  0  4  0  4  4  0  0  0  0  4  0  4  0  0  0  4  4  4  4  0  4  4  4  0  4  0  0  4  0  0
 0  0  0  0  0  0  4  0  0  0  0  0  0  4  0  4  4  0  0  4  0  4  0  0  4  0  4  4  4  0  4  4  0  4  0  4  4  0  4  4  4  4  4  0  0  4  0  0  0  4  4  4  0  0  0  0
 0  0  0  0  0  0  0  4  4  4  0  4  4  4  0  4  4  4  0  4  4  4  4  0  0  4  4  4  4  4  4  0  4  0  0  0  4  4  0  0  4  4  0  4  0  0  4  0  0  4  4  4  4  0  0  0

generates a code of length 56 over Z8 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+30x^44+106x^45+272x^46+514x^47+861x^48+1632x^49+2116x^50+2868x^51+3810x^52+4930x^53+5886x^54+6226x^55+6651x^56+6452x^57+6096x^58+5038x^59+3977x^60+2968x^61+1958x^62+1340x^63+740x^64+498x^65+283x^66+134x^67+54x^68+52x^69+28x^70+8x^71+3x^72+2x^73+1x^76+1x^82

The gray image is a code over GF(2) with n=224, k=16 and d=88.
This code was found by Heurico 1.16 in 99.9 seconds.