The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^44+76x^45+147x^46+208x^47+237x^48+238x^49+233x^50+216x^51+252x^52+286x^53+243x^54+306x^55+268x^56+240x^57+196x^58+224x^59+174x^60+148x^61+144x^62+60x^63+58x^64+34x^65+26x^66+8x^67+12x^68+2x^69+2x^70+2x^71+1x^74

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 1.72 seconds.