The generator matrix

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

generates a code of length 90 over F4[X]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+63x^244+252x^248+366x^252+384x^256+48x^258+408x^260+576x^262+444x^264+2592x^266+360x^268+5184x^270+318x^272+3888x^274+294x^276+270x^280+222x^284+186x^288+147x^292+144x^296+105x^300+42x^304+48x^308+27x^312+3x^316+9x^320+3x^344

The gray image is a linear code over GF(4) with n=360, k=7 and d=244.
This code was found by Heurico 1.16 in 4.29 seconds.