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.