The generator matrix

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

generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+96x^39+201x^40+792x^41+96x^42+864x^43+480x^44+1464x^45+576x^46+2592x^47+1053x^48+2376x^49+864x^50+2592x^51+768x^52+1512x^53+51x^56+6x^64

The gray image is a linear code over GF(4) with n=64, k=7 and d=39.
This code was found by Heurico 1.16 in 8.78 seconds.