The generator matrix

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

generates a code of length 18 over F4[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+81x^36+249x^40+288x^42+372x^44+384x^45+2304x^46+474x^48+3456x^49+7488x^50+690x^52+10368x^53+13824x^54+876x^56+10368x^57+12960x^58+828x^60+333x^64+141x^68+51x^72

The gray image is a linear code over GF(4) with n=72, k=8 and d=36.
This code was found by Heurico 1.16 in 3.39 seconds.