The generator matrix

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

generates a code of length 76 over F4[X]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+186x^220+600x^221+315x^224+1344x^225+267x^228+240x^229+18x^232+288x^233+96x^236+312x^237+60x^240+288x^241+69x^244+6x^248+3x^252+3x^268

The gray image is a linear code over GF(4) with n=304, k=6 and d=220.
This code was found by Heurico 1.16 in 0.404 seconds.