The generator matrix

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

generates a code of length 17 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+168x^37+228x^38+168x^39+1116x^40+1704x^41+2112x^42+2016x^43+4713x^44+8016x^45+10680x^46+9072x^47+17442x^48+26256x^49+29040x^50+18144x^51+28647x^52+35592x^53+29316x^54+13608x^55+13440x^56+8136x^57+2352x^58+135x^60+33x^64+9x^68

The gray image is a linear code over GF(4) with n=68, k=9 and d=37.
This code was found by Heurico 1.16 in 34.8 seconds.