The generator matrix

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

generates a code of length 17 over F4[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+192x^40+456x^41+384x^42+1116x^43+1593x^44+2100x^45+1596x^46+3564x^47+4221x^48+4788x^49+4140x^50+9492x^51+8460x^52+7644x^53+4212x^54+5796x^55+3414x^56+1908x^57+420x^58+21x^60+12x^64+6x^68

The gray image is a linear code over GF(4) with n=68, k=8 and d=40.
This code was found by Heurico 1.16 in 3.05 seconds.