The generator matrix

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

generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+288x^35+381x^36+600x^37+1224x^38+2220x^39+4104x^40+2880x^41+4704x^42+10608x^43+17586x^44+12720x^45+18864x^46+29160x^47+35235x^48+24960x^49+26208x^50+28560x^51+26457x^52+7992x^53+4296x^54+2892x^55+126x^56+72x^60+6x^64

The gray image is a linear code over GF(4) with n=64, k=9 and d=35.
This code was found by Heurico 1.16 in 31.2 seconds.