The generator matrix

 1  0  0  0  1  1  1  1  1  1 a^2*X  1  1  1  1  1
 0  1  0  0  X  1 X+1 a^2*X+a  0 a*X+a  1  1  a a^2*X+1 a*X+a^2  X
 0  0  1  0 a^2*X+1  1 a^2*X  a X+a a^2*X+a^2 a*X+a a*X+1  X  X a*X+a^2 X+1
 0  0  0  1 a^2  X a*X+a^2 X+1 a*X+a  0 a^2*X+a^2 a*X+1 a^2*X X+a X+1 a*X+1

generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+252x^37+420x^38+120x^39+990x^40+1776x^41+2028x^42+1080x^43+2985x^44+5544x^45+5796x^46+3240x^47+7512x^48+11376x^49+8292x^50+3240x^51+4842x^52+4092x^53+1896x^54+30x^56+21x^60+3x^64

The gray image is a linear code over GF(4) with n=64, k=8 and d=37.
This code was found by Heurico 1.16 in 2.75 seconds.