The generator matrix

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

generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+264x^37+432x^38+120x^39+990x^40+1824x^41+2076x^42+1080x^43+2985x^44+5328x^45+5580x^46+3240x^47+7512x^48+11616x^49+8532x^50+3240x^51+4842x^52+4008x^53+1812x^54+30x^56+21x^60+3x^64

The gray image is a linear code over GF(4) with n=64, k=8 and d=37.
This code was found by Heurico 1.16 in 2.68 seconds.