The generator matrix

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

generates a code of length 17 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+84x^41+72x^42+144x^43+825x^44+408x^45+648x^46+432x^47+1155x^48+864x^49+1944x^50+1776x^51+2304x^52+1320x^53+1944x^54+720x^55+1302x^56+396x^57+33x^60+6x^64+6x^68

The gray image is a linear code over GF(4) with n=68, k=7 and d=41.
This code was found by Heurico 1.16 in 0.167 seconds.