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

generates a code of length 17 over F4[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+192x^41+36x^42+144x^43+504x^44+804x^45+324x^46+432x^47+1059x^48+2052x^49+972x^50+1008x^51+2499x^52+3084x^53+972x^54+720x^55+762x^56+780x^57+18x^60+18x^64+3x^68

The gray image is a linear code over GF(4) with n=68, k=7 and d=41.
This code was found by Heurico 1.16 in 0.218 seconds.