The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+38x^40+147x^42+351x^44+565x^46+790x^48+1067x^50+1133x^52+1144x^54+1100x^56+817x^58+537x^60+285x^62+117x^64+62x^66+27x^68+6x^70+2x^72+2x^74+1x^82

The gray image is a code over GF(2) with n=106, k=13 and d=40.
This code was found by Heurico 1.16 in 7.39 seconds.