The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+38x^37+124x^38+234x^39+428x^40+634x^41+922x^42+1254x^43+1577x^44+2068x^45+2488x^46+3080x^47+3534x^48+4108x^49+4635x^50+4798x^51+5157x^52+4852x^53+4575x^54+4372x^55+3858x^56+3336x^57+2636x^58+2070x^59+1587x^60+1136x^61+743x^62+508x^63+337x^64+192x^65+103x^66+54x^67+31x^68+18x^69+29x^70+14x^71+2x^72+2x^73+1x^78

The gray image is a code over GF(2) with n=104, k=16 and d=37.
This code was found by Heurico 1.10 in 147 seconds.