The generator matrix

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

generates a code of length 17 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+180x^36+96x^39+333x^40+576x^42+1152x^43+489x^44+5184x^46+5184x^47+669x^48+15552x^50+10368x^51+957x^52+15552x^54+7776x^55+807x^56+459x^60+174x^64+27x^68

The gray image is a linear code over GF(4) with n=68, k=8 and d=36.
This code was found by Heurico 1.16 in 3.62 seconds.