The generator matrix

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

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+201x^40+792x^41+96x^42+864x^43+480x^44+1464x^45+576x^46+2592x^47+1053x^48+2376x^49+864x^50+2592x^51+768x^52+1512x^53+51x^56+6x^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 8.94 seconds.