The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+39x^44+64x^45+95x^46+120x^47+141x^48+134x^49+130x^50+154x^51+138x^52+126x^53+116x^54+122x^55+112x^56+122x^57+107x^58+94x^59+65x^60+58x^61+49x^62+22x^63+10x^64+8x^65+10x^66+6x^68+4x^70+1x^74

The gray image is a code over GF(2) with n=106, k=11 and d=44.
This code was found by Heurico 1.16 in 0.472 seconds.