The generator matrix

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

generates a code of length 17 over F4[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+186x^36+48x^39+540x^40+384x^42+576x^43+1521x^44+768x^45+3456x^46+2592x^47+3954x^48+4608x^49+10368x^50+5184x^51+5787x^52+6912x^53+10368x^54+3888x^55+3744x^56+447x^60+177x^64+27x^68

The gray image is a linear code over GF(4) with n=68, k=8 and d=36.
This code was found by Heurico 1.16 in 3.38 seconds.