The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^40+130x^41+234x^42+394x^43+480x^44+574x^45+614x^46+734x^47+928x^48+1038x^49+1048x^50+1158x^51+1273x^52+1228x^53+1220x^54+1122x^55+988x^56+848x^57+637x^58+556x^59+376x^60+232x^61+196x^62+120x^63+81x^64+40x^65+16x^66+12x^67+15x^68+6x^69+2x^70+1x^72+1x^74

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 52 seconds.