The generator matrix

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

generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+93x^36+96x^39+456x^40+192x^42+864x^43+1455x^44+1152x^46+2592x^47+2802x^48+1728x^50+2592x^51+2139x^52+156x^56+57x^60+9x^64

The gray image is a linear code over GF(4) with n=64, k=7 and d=36.
This code was found by Heurico 1.16 in 0.228 seconds.