The generator matrix

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

generates a code of length 18 over F4[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+300x^40+264x^41+372x^42+660x^43+2655x^44+1896x^45+3072x^46+3072x^47+10380x^48+8352x^49+12120x^50+11400x^51+30591x^52+20832x^53+33264x^54+19104x^55+40128x^56+21144x^57+18132x^58+8772x^59+12045x^60+2808x^61+624x^62+123x^64+21x^68+12x^72

The gray image is a linear code over GF(4) with n=72, k=9 and d=40.
This code was found by Heurico 1.16 in 41.8 seconds.