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

generates a code of length 91 over F4[X]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+108x^248+318x^252+378x^256+60x^259+420x^260+420x^263+384x^264+1560x^267+357x^268+3720x^271+381x^272+4332x^275+267x^276+2196x^279+321x^280+294x^284+186x^288+186x^292+177x^296+105x^300+90x^304+48x^308+42x^312+18x^316+12x^320+3x^340

The gray image is a linear code over GF(4) with n=364, k=7 and d=248.
This code was found by Heurico 1.16 in 4.38 seconds.