The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  0  1 aX
 0  1  0  0  X (a+1)X  1 (a+1)X+a a+1 (a+1)X+1  a  a X+a  1 X+a+1  1
 0  0  1  1 (a+1)X+a a+1 a+1 X+a+1 X+a+1  a  a  0 X+a X+a aX+1 (a+1)X+1
 0  0  0 (a+1)X  X  0 aX aX (a+1)X  X (a+1)X  X aX (a+1)X  0  0

generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+96x^39+183x^40+816x^41+96x^42+864x^43+531x^44+1392x^45+576x^46+2592x^47+1002x^48+2448x^49+864x^50+2592x^51+798x^52+1488x^53+27x^56+15x^60+3x^64

The gray image is a linear code over GF(4) with n=64, k=7 and d=39.
This code was found by Heurico 1.16 in 29.3 seconds.