The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  2  1  1  1  1  2  2  0  0  2  0  2  1  1  1  1  2  2  1  1  2  1  2  2  0  1  0  2  2  1  2  1  1  1  2  2  0  0  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  3  1  2  1  0  2  3  1  1  1  0  0  1  1  1  3  0  3  2  1  0  3  1  1  0  1  2  1  3  1  2  1  3  0  1  3  0  1  1  1  1  2  2  0  3
 0  0  1  1  1  0  1  0  1  1  0  2  1  3  3  2  0  3  2  3  1  1  2  0  1  0  0  1  1  0  1  2  1  3  2  1  1  1  0  0  1  0  0  1  3  1  2  1  3  0  2  0  3  1  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  2  2  0  0  2  0  2  0  0  0  2  2  2  0  0  0  0  2  0  0  0  2  0  0  2  0  2  2  0  2  2  2
 0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  0  0  0  2  2  0  2  0  2  0  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2  2  0  0  0  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  2  2  2  0  2  0  0  2  0  2  2  0  0  2  0  0  0  2  0  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  2  0  0  2  2  0  2  2  2  2  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  2  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  0  2  2  2  2  2  2  0  0  2
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2  2  0  2  0  0  0  2  0  0  2  0  2  2  0  2  2  0  2  2  2  2  2  2  0  2  0  0  0  0  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  2  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  0  0  2  2  0  0  0  2  2  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+167x^44+326x^46+699x^48+704x^50+1065x^52+1054x^54+1272x^56+968x^58+965x^60+442x^62+351x^64+88x^66+71x^68+2x^70+12x^72+4x^76+1x^80

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 8.42 seconds.