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

generates a code of length 87 over F4[X]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+69x^236+303x^240+12x^242+387x^244+192x^246+402x^248+432x^250+480x^252+1308x^254+339x^256+2892x^258+372x^260+3672x^262+318x^264+3000x^266+312x^268+780x^270+222x^272+246x^276+171x^280+135x^284+135x^288+75x^292+75x^296+24x^300+12x^304+12x^308+6x^312

The gray image is a linear code over GF(4) with n=348, k=7 and d=236.
This code was found by Heurico 1.16 in 4.15 seconds.