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

generates a code of length 92 over F4[X]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+168x^252+354x^256+384x^260+60x^262+399x^264+420x^266+402x^268+1560x^270+363x^272+3720x^274+336x^276+4332x^278+294x^280+2196x^282+360x^284+234x^288+207x^292+150x^296+129x^300+114x^304+81x^308+48x^312+33x^316+18x^320+12x^324+6x^328+3x^344

The gray image is a linear code over GF(4) with n=368, k=7 and d=252.
This code was found by Heurico 1.16 in 4.46 seconds.