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

generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+225x^244+327x^248+465x^252+48x^253+387x^256+432x^257+420x^260+1632x^261+390x^264+3552x^265+285x^268+4464x^269+315x^272+2160x^273+261x^276+231x^280+198x^284+183x^288+135x^292+105x^296+93x^300+30x^304+27x^308+15x^312+3x^332

The gray image is a linear code over GF(4) with n=356, k=7 and d=244.
This code was found by Heurico 1.16 in 18.9 seconds.