The generator matrix

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

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+132x^40+150x^44+168x^48+3072x^51+186x^52+204x^56+138x^60+39x^64+6x^68

The gray image is a linear code over GF(4) with n=68, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0338 seconds.