The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  1  X  1  1  1  1
 0  1  0  0  X  1 X+1  1 a*X  1 a^2 X+a  1  1 X+1  0 X+a^2 a^2*X+a
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 a^2*X+a a^2*X+a^2 a*X a*X+a X+a a*X+a^2 a^2*X a^2*X+a a^2*X+1
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2  a a^2*X a^2*X+1  1 a*X+1 a^2*X+a^2 X+a X+a a^2*X+a^2  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+1272x^44+1440x^46+4674x^48+4320x^50+12528x^52+11616x^54+17322x^56+7200x^58+5112x^60+45x^64+6x^72

The gray image is a linear code over GF(4) with n=72, k=8 and d=44.
This code was found by Heurico 1.16 in 32.5 seconds.