The generator matrix

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

generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+708x^38+1938x^40+3312x^42+6480x^44+9432x^46+16110x^48+14448x^50+10224x^52+2820x^54+54x^56+9x^64

The gray image is a linear code over GF(4) with n=64, k=8 and d=38.
This code was found by Heurico 1.16 in 81.2 seconds.