The generator matrix

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

generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+144x^43+945x^44+408x^45+288x^47+663x^48+144x^49+336x^51+948x^52+216x^53+3x^60

The gray image is a linear code over GF(4) with n=64, k=6 and d=43.
This code was found by Heurico 1.16 in 0.094 seconds.