The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1 a^2*X  1  0  1  X  1 a*X  1  1  1  1 a^2*X  1  1  1 a*X  1  1  1  1  1  1  1  1  1  1  0  1  1  1 a^2*X  1  X  1  1 a^2*X  1  1 a*X  1  1  1  1  1  1  1  1  1  1  1  1 a*X  1  1  1  1  0  1
 0  1  0 a^2*X a*X  X  1 a^2*X+a a^2 a^2*X+1 a*X+1 X+1 a*X+a  1 X+a^2 X+a a^2*X+a^2  a  1 a*X+a^2  1  a  1  0  1 a*X+1 a^2*X X+a^2 a^2  1 X+1 a^2*X+a  X  0 a*X+a^2 a^2*X+a X+a a^2 a*X+1 a^2*X a*X+a^2  1 a*X+a X+a^2  1 a^2*X+a^2  1 a*X  1  a  1 a*X+a^2  0  1 a^2*X+a^2 a*X+a  1 X+a a^2*X+1 a*X+a^2  1 a^2 X+a X+a^2  X a*X  X  0 a^2  1 X+a X+1 X+1 a*X+a^2  1 a*X
 0  0  1  1  a a^2 X+a^2 a^2*X+a^2 a*X+a^2 X+a a*X+1  X X+1 a^2*X+a^2 a*X+a a^2*X+a a^2*X+1  0 a*X+1 a*X X+a  X a^2*X+a a*X a^2*X+1 X+a^2 a^2*X+1 a*X+1 a*X+a  X X+a a^2*X+a a^2*X+a^2  1 X+a^2  X  1 a^2*X+1  0 a^2 a^2*X+a a*X+a X+a  a  1 X+1 a^2 a^2*X a^2*X  1 a*X+a  a  1  1 a*X+a^2 a*X+1  X X+a  X a^2*X+a^2  0 a^2*X+a a^2*X X+1 a^2*X X+a^2  0 a*X+1 X+1 a^2*X+a a*X+a a*X+a^2 X+1 a^2*X a^2*X  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+192x^220+324x^221+48x^222+360x^223+615x^224+504x^225+96x^226+264x^227+357x^228+180x^229+168x^231+147x^232+108x^233+12x^234+120x^235+93x^236+84x^237+24x^238+12x^239+117x^240+48x^241+12x^242+24x^243+39x^244+84x^245+12x^247+36x^248+12x^249+3x^276

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 0.14 seconds.