The generator matrix

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

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+144x^36+432x^40+192x^42+456x^44+1728x^46+588x^48+5184x^50+912x^52+5184x^54+1008x^56+360x^60+147x^64+48x^68

The gray image is a linear code over GF(4) with n=68, k=7 and d=36.
This code was found by Heurico 1.16 in 0.436 seconds.