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

generates a code of length 86 over F4[X]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+66x^232+267x^236+384x^240+12x^243+411x^244+180x^247+375x^248+1080x^251+384x^252+3240x^255+351x^256+4860x^259+270x^260+2916x^263+273x^264+306x^268+291x^272+195x^276+189x^280+117x^284+120x^288+54x^292+21x^296+6x^300+9x^304+3x^308+3x^324

The gray image is a linear code over GF(4) with n=344, k=7 and d=232.
This code was found by Heurico 1.16 in 4.06 seconds.