The generator matrix

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

generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+84x^32+12x^33+288x^36+180x^37+576x^39+516x^40+1080x^41+768x^42+5184x^43+552x^44+3240x^45+4608x^46+15552x^47+936x^48+4860x^49+6912x^50+15552x^51+912x^52+2916x^53+588x^56+168x^60+51x^64

The gray image is a linear code over GF(4) with n=64, k=8 and d=32.
This code was found by Heurico 1.16 in 2.77 seconds.