The generator matrix

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

generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+780x^38+264x^39+783x^40+1152x^41+2340x^42+2376x^43+2769x^44+3168x^45+6444x^46+7128x^47+5475x^48+7488x^49+9228x^50+7128x^51+4242x^52+2016x^53+2712x^54+21x^56+21x^60

The gray image is a linear code over GF(4) with n=64, k=8 and d=38.
This code was found by Heurico 1.16 in 77.1 seconds.