The generator matrix

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

generates a code of length 17 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+84x^39+363x^40+468x^41+240x^42+1008x^43+1140x^44+1392x^45+2160x^46+4536x^47+3465x^48+5112x^49+6480x^50+9072x^51+5070x^52+6768x^53+6480x^54+6804x^55+3093x^56+1620x^57+120x^60+54x^64+6x^68

The gray image is a linear code over GF(4) with n=68, k=8 and d=39.
This code was found by Heurico 1.16 in 3.59 seconds.