The generator matrix

 1  0  0  0  0  1  1  1  2  0  1  1  1  0  0  1  1  2  2  1  1  2  0  1  0  2  0  0  1  1  1  2  1  1  1  1  1  1  2  1  2  1  0  1  1  1  0  1  0  2  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  2  2  2  1  1  3  1  0  2  1  0  1  1  1  3  0  2  1  0  1  1  3  1  0  2  0  2  0  1  0  0  2  2  2  1  2  0  1  3  0
 0  0  1  0  0  0  1  1  1  1  3  2  0  0  1  3  1  1  0  3  2  1  2  2  2  2  2  0  0  0  1  3  3  3  3  2  3  3  1  3  1  1  1  3  3  0  0  1  3  1  3  1  1  0
 0  0  0  1  0  1  1  0  3  1  2  3  0  3  0  3  2  2  0  1  1  3  2  0  1  2  2  3  0  2  3  3  2  2  0  3  2  1  2  3  1  2  3  3  0  2  0  3  2  3  0  2  1  0
 0  0  0  0  1  1  0  1  1  2  2  0  3  1  0  2  1  1  2  3  2  3  1  1  2  0  1  2  0  3  3  3  2  0  1  1  3  0  2  1  0  1  3  3  3  3  1  0  2  0  0  0  0  0
 0  0  0  0  0  2  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0
 0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  0  2  2  2  0  2  2  2  2  0  0  2  2  0  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+49x^44+84x^45+146x^46+192x^47+241x^48+246x^49+224x^50+260x^51+246x^52+268x^53+243x^54+274x^55+290x^56+230x^57+206x^58+218x^59+193x^60+150x^61+114x^62+70x^63+52x^64+44x^65+26x^66+10x^67+16x^68+2x^69+1x^70

The gray image is a code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 1.74 seconds.