The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+50x^45+109x^46+126x^47+156x^48+154x^49+158x^50+154x^51+136x^52+124x^53+125x^54+128x^55+106x^56+112x^57+89x^58+76x^59+56x^60+58x^61+46x^62+26x^63+21x^64+14x^65+17x^66+2x^67+4x^68

The gray image is a code over GF(2) with n=106, k=11 and d=45.
This code was found by Heurico 1.16 in 0.441 seconds.