The generator matrix
1 0 1 1 1 1 1 1 1 0 1 1 1 0 X 1 1
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1 0 a (a+1)X+1 1 X (a+1)X+a+1 aX+a+1
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 X X (a+1)X 0 aX
0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X 0 aX aX 0 (a+1)X
generates a code of length 17 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 43.
Homogenous weight enumerator: w(x)=1x^0+192x^43+168x^44+576x^47+240x^48+1344x^51+360x^52+960x^55+192x^56+48x^60+15x^64
The gray image is a linear code over GF(4) with n=68, k=6 and d=43.
This code was found by Heurico 1.16 in 0.0179 seconds.