The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  X
 0  X  0  0  0  0  0  X  X a*X  X  X  0  X  0  X  X
 0  0  X  0  0  0  X a^2*X a^2*X  0 a*X a*X  0  X a^2*X  X a*X
 0  0  0  X  0  0 a^2*X  X  0 a*X a^2*X a*X a*X  0 a^2*X a*X  X
 0  0  0  0  X  0  X a^2*X a*X a^2*X  0  X  X a^2*X  X  0 a*X
 0  0  0  0  0  X a^2*X  X a^2*X a^2*X a*X a^2*X  X a^2*X a*X a^2*X a*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+144x^36+432x^40+192x^42+456x^44+1728x^46+588x^48+5184x^50+912x^52+5184x^54+1008x^56+360x^60+147x^64+48x^68

The gray image is a linear code over GF(4) with n=68, k=7 and d=36.
This code was found by Heurico 1.16 in 0.432 seconds.