The generator matrix

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

generates a code of length 17 over F4[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+84x^39+363x^40+468x^41+240x^42+1008x^43+1140x^44+1392x^45+2160x^46+4536x^47+3465x^48+5112x^49+6480x^50+9072x^51+5070x^52+6768x^53+6480x^54+6804x^55+3093x^56+1620x^57+120x^60+54x^64+6x^68

The gray image is a linear code over GF(4) with n=68, k=8 and d=39.
This code was found by Heurico 1.16 in 3.43 seconds.