The generator matrix

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

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+72x^36+156x^40+174x^44+3282x^48+180x^52+168x^56+54x^60+9x^64

The gray image is a linear code over GF(4) with n=64, k=6 and d=36.
This code was found by Heurico 1.16 in 0.0286 seconds.