The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  2  1  1  0  0  1  1  0  1  2  1  1  1  2  2  1  0  1  0  2  1  0  1  0  1  1  1  0  1  1  1  1  2  1  0  2  2  0  0  1  1  2  2  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  1  1  3  2  1  3  1  3  2  2  2  0  3  1  2  0  1  2  1  0  2  0  3  2  1  3  1  3  0  2  3  0  1  2  2  1  1  0  1  1  2
 0  0  1  0  0  0  1  1  1  0  2  0  1  3  1  1  0  1  0  2  2  2  0  3  1  1  1  1  3  1  1  0  1  3  0  0  3  3  2  0  0  0  3  2  1  2  2  1  2  1  3  2  0  0  0
 0  0  0  1  0  1  1  0  1  1  0  3  2  3  2  1  2  0  0  3  1  1  1  2  1  2  0  2  1  1  1  3  1  2  1  1  3  0  1  2  1  1  1  1  1  2  3  3  1  2  0  0  2  0  0
 0  0  0  0  1  1  0  1  1  2  3  3  0  1  3  0  3  1  0  2  3  0  3  3  3  2  1  0  3  2  1  2  1  2  1  2  0  0  2  0  1  3  0  2  3  1  1  2  2  1  1  3  1  2  1
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  2  0  0  2  2  0  0  2  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  0  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  2  0  2  0  0  2  0  0  2  0  2  2  2  0  0  0  0  2  2  0  2  2  2  2  0  2  2  2  2  0  2  0  2  2  2  2  2  2
 0  0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  0  0  0  2  2  2  0  0  0  2  0  2  2  2  2  0  0  2  0  2

generates a code of length 55 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+64x^44+120x^45+188x^46+302x^47+316x^48+346x^49+420x^50+468x^51+525x^52+526x^53+567x^54+558x^55+542x^56+566x^57+498x^58+454x^59+424x^60+406x^61+292x^62+216x^63+139x^64+72x^65+74x^66+46x^67+35x^68+12x^69+9x^70+4x^71+1x^72+1x^88

The gray image is a code over GF(2) with n=110, k=13 and d=44.
This code was found by Heurico 1.16 in 8.03 seconds.