The generator matrix

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

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+72x^36+255x^40+372x^44+495x^48+702x^52+12288x^54+879x^56+696x^60+432x^64+174x^68+18x^72

The gray image is a linear code over GF(4) with n=72, k=7 and d=36.
This code was found by Heurico 1.16 in 0.42 seconds.