The generator matrix

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

generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+288x^35+372x^36+912x^37+780x^38+2604x^39+3015x^40+4032x^41+3792x^42+12624x^43+13989x^44+16224x^45+17352x^46+33480x^47+27294x^48+28608x^49+24528x^50+33840x^51+20670x^52+11664x^53+2700x^54+3180x^55+123x^56+57x^60+15x^64

The gray image is a linear code over GF(4) with n=64, k=9 and d=35.
This code was found by Heurico 1.16 in 34.6 seconds.