The generator matrix

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

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+72x^32+12x^33+336x^36+180x^37+576x^39+444x^40+1080x^41+768x^42+5184x^43+612x^44+3240x^45+4608x^46+15552x^47+876x^48+4860x^49+6912x^50+15552x^51+984x^52+2916x^53+540x^56+180x^60+51x^64

The gray image is a linear code over GF(4) with n=64, k=8 and d=32.
This code was found by Heurico 1.16 in 2.77 seconds.