The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^44+28x^45+45x^46+88x^47+80x^48+84x^49+73x^50+48x^51+52x^52+68x^53+54x^54+88x^55+50x^56+76x^57+57x^58+32x^59+14x^60+16x^62+5x^64+5x^66+2x^68+4x^70+1x^74+1x^78

The gray image is a code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in 0.149 seconds.