The generator matrix

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

generates a code of length 17 over F4[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+108x^37+252x^38+168x^39+1116x^40+1908x^41+2040x^42+2016x^43+4713x^44+7800x^45+10728x^46+9072x^47+17442x^48+26280x^49+29088x^50+18144x^51+28647x^52+35676x^53+29244x^54+13608x^55+13440x^56+8100x^57+2376x^58+135x^60+33x^64+9x^68

The gray image is a linear code over GF(4) with n=68, k=9 and d=37.
This code was found by Heurico 1.16 in 38 seconds.