The generator matrix

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

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+51x^40+48x^42+60x^43+129x^44+144x^45+288x^46+240x^47+153x^48+1296x^49+576x^50+840x^51+165x^52+3888x^53+864x^54+1200x^55+195x^56+3888x^57+1296x^58+732x^59+147x^60+138x^64+39x^68+6x^72

The gray image is a linear code over GF(4) with n=72, k=7 and d=40.
This code was found by Heurico 1.16 in 0.259 seconds.