The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  4  0  0  4  2  0  1  2  2  2  4  2  1  1  1  1  1  0  2  1  2  1  0  4  4  1  4  2  2  2  1
 0  2  0  0  0  2  6  2  0  4  0  2  0  0  2  6  6  4  6  4  2  4  2  4  6  2  2  2  2  2  0  2  0  2  4  0  4  4  6  6  0  6  2  6  4  4  0  0  0  2  0  2  6  6  4  0
 0  0  2  0  2  2  6  0  0  0  2  4  0  6  6  2  4  4  4  6  2  6  2  0  0  4  6  4  4  2  2  6  6  0  4  0  4  6  4  6  6  6  6  2  0  6  0  2  0  0  6  4  2  6  4  0
 0  0  0  2  2  0  6  2  0  2  2  2  4  4  4  6  4  2  2  2  0  0  2  2  0  6  2  4  2  0  0  0  0  6  6  2  6  2  2  6  0  0  2  6  4  6  4  4  2  4  6  4  6  2  0  0
 0  0  0  0  4  0  0  0  0  0  0  0  0  0  4  4  0  4  4  0  4  0  4  4  4  4  0  0  4  4  4  0  0  0  0  4  4  4  0  0  0  0  4  0  0  4  4  0  4  4  0  4  4  4  4  0
 0  0  0  0  0  4  0  0  0  0  4  4  4  0  0  0  0  0  0  0  4  4  4  0  0  4  4  0  4  0  4  0  4  4  4  0  0  4  4  4  0  0  4  4  4  4  4  4  0  0  4  4  0  4  0  0
 0  0  0  0  0  0  4  0  0  4  4  4  0  0  4  0  4  0  4  0  0  4  4  4  0  0  0  0  4  4  4  4  0  4  4  4  0  4  0  4  0  4  4  0  0  0  0  4  4  4  4  4  0  0  0  0
 0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  0  4  4  4  0  4  0  4  0  4  0  4  4  0  0  4  0
 0  0  0  0  0  0  0  0  4  0  0  0  0  4  4  0  4  4  0  0  0  4  4  4  0  0  4  4  4  4  0  4  4  0  0  0  4  4  0  0  4  0  0  0  0  4  0  4  4  4  0  0  0  4  4  0

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

Homogenous weight enumerator: w(x)=1x^0+75x^44+58x^45+157x^46+172x^47+287x^48+430x^49+591x^50+710x^51+921x^52+1148x^53+1262x^54+1588x^55+1544x^56+1592x^57+1356x^58+1136x^59+963x^60+718x^61+557x^62+408x^63+231x^64+138x^65+147x^66+74x^67+55x^68+12x^69+24x^70+8x^71+16x^72+2x^74+2x^76+1x^80

The gray image is a code over GF(2) with n=224, k=14 and d=88.
This code was found by Heurico 1.16 in 13.4 seconds.