The generator matrix

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

generates a code of length 54 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+52x^44+118x^46+175x^48+279x^50+288x^52+257x^54+292x^56+258x^58+163x^60+84x^62+39x^64+23x^66+7x^68+5x^70+4x^72+1x^76+1x^80+1x^84

The gray image is a code over GF(2) with n=108, k=11 and d=44.
This code was found by Heurico 1.16 in 0.554 seconds.