The generator matrix

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

generates a code of length 55 over Z8 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+11x^34+50x^35+64x^36+120x^37+175x^38+216x^39+305x^40+480x^41+650x^42+798x^43+925x^44+946x^45+1014x^46+1120x^47+1204x^48+1662x^49+1963x^50+2968x^51+3926x^52+4986x^53+6140x^54+6052x^55+6124x^56+4962x^57+4019x^58+3064x^59+1964x^60+1626x^61+1085x^62+1116x^63+1079x^64+976x^65+898x^66+720x^67+623x^68+524x^69+371x^70+238x^71+143x^72+88x^73+51x^74+40x^75+25x^76+14x^77+7x^78+2x^79+1x^84

The gray image is a code over GF(2) with n=220, k=16 and d=68.
This code was found by Heurico 1.16 in 99.9 seconds.