The generator matrix

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

generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+81x^36+192x^39+306x^40+1728x^43+822x^44+5184x^47+1497x^48+5184x^51+1173x^52+132x^56+84x^60

The gray image is a linear code over GF(4) with n=64, k=7 and d=36.
This code was found by Heurico 1.16 in 0.23 seconds.