The generator matrix

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

generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+81x^32+312x^36+462x^40+768x^42+612x^44+4608x^46+864x^48+6912x^50+1008x^52+522x^56+180x^60+54x^64

The gray image is a linear code over GF(4) with n=64, k=7 and d=32.
This code was found by Heurico 1.16 in 0.366 seconds.