The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+62x^42+64x^43+94x^44+162x^45+283x^46+196x^47+217x^48+284x^49+314x^50+350x^51+195x^52+288x^53+307x^54+268x^55+143x^56+228x^57+218x^58+128x^59+89x^60+62x^61+81x^62+16x^63+22x^64+14x^66+2x^67+5x^68+1x^70+1x^72+1x^76

The gray image is a code over GF(2) with n=104, k=12 and d=42.
This code was found by Heurico 1.16 in 2.02 seconds.