The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+91x^40+122x^41+247x^42+330x^43+482x^44+518x^45+672x^46+850x^47+891x^48+1026x^49+1109x^50+1182x^51+1153x^52+1272x^53+1160x^54+1112x^55+991x^56+890x^57+647x^58+522x^59+397x^60+226x^61+228x^62+86x^63+72x^64+42x^65+27x^66+14x^67+15x^68+4x^70+2x^72+2x^74+1x^76

The gray image is a code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.16 in 49.8 seconds.