The generator matrix

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

generates a code of length 79 over F4[X]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+528x^225+804x^226+324x^227+48x^228+1056x^229+1224x^230+444x^231+63x^232+1596x^233+1488x^234+468x^235+42x^236+996x^237+1044x^238+372x^239+27x^240+1212x^241+1068x^242+348x^243+27x^244+816x^245+588x^246+228x^247+21x^248+444x^249+468x^250+108x^251+18x^252+204x^253+168x^254+12x^255+60x^257+60x^258+6x^260+3x^276

The gray image is a linear code over GF(4) with n=316, k=7 and d=225.
This code was found by Heurico 1.16 in 3.98 seconds.