The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  X  0  X
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1 a^2*X+a^2  X  1  1
 0  0 a^2*X  0  X  0  X a*X a*X a*X a*X  X a^2*X a^2*X a^2*X  0  X
 0  0  0  X a*X a*X  0 a*X  X  X  0  X a*X  X a*X a*X  0

generates a code of length 17 over F4[X]/(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 0.018 seconds.