The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  1  2  1  2  2  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  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  0  0  0  0  0  0  0  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  0  0  0  0  2  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  2  2  2  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  2  0  2  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  0  0  2  2  0  2  0  0  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  2  2  0  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  2  0  0  2  2  0  0  2  0  0  2  2  2  0  0

generates a code of length 37 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+87x^20+334x^24+776x^28+1675x^32+1280x^34+4574x^36+2560x^38+3028x^40+256x^42+1040x^44+570x^48+179x^52+22x^56+2x^64

The gray image is a code over GF(2) with n=74, k=14 and d=20.
This code was found by Heurico 1.16 in 13.4 seconds.