The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+44x^44+112x^45+146x^46+144x^47+148x^48+146x^49+126x^50+148x^51+153x^52+130x^53+133x^54+124x^55+86x^56+86x^57+71x^58+70x^59+62x^60+32x^61+33x^62+24x^63+17x^64+4x^65+3x^66+2x^67+1x^68+2x^69

The gray image is a code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 0.417 seconds.