The generator matrix

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

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+183x^36+120x^37+288x^38+288x^39+1452x^40+480x^41+1104x^42+2592x^43+6012x^44+1680x^45+4176x^46+7776x^47+11835x^48+2400x^49+5616x^50+7776x^51+8967x^52+1464x^53+1104x^54+162x^56+54x^60+6x^64

The gray image is a linear code over GF(4) with n=64, k=8 and d=36.
This code was found by Heurico 1.16 in 2.98 seconds.