The generator matrix

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

generates a code of length 18 over F4[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+132x^44+84x^45+84x^46+432x^47+1143x^48+504x^49+324x^50+624x^51+2625x^52+1152x^53+636x^54+1296x^55+3882x^56+1224x^57+492x^58+720x^59+882x^60+108x^61+30x^64+9x^68

The gray image is a linear code over GF(4) with n=72, k=7 and d=44.
This code was found by Heurico 1.16 in 0.187 seconds.