The generator matrix

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

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+186x^36+96x^37+288x^38+288x^39+1446x^40+576x^41+1104x^42+2592x^43+6009x^44+1536x^45+4176x^46+7776x^47+11847x^48+2496x^49+5616x^50+7776x^51+8964x^52+1440x^53+1104x^54+156x^56+57x^60+6x^64

The gray image is a linear code over GF(4) with n=64, k=8 and d=36.
This code was found by Heurico 1.16 in 2.88 seconds.