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  1  1  1  1  1  1 a^2*X  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^2*X+a  X a^2*X X+a^2 a^2*X+a  X a*X+1 a^2*X+1 X+1  1 a^2*X+1 a*X+a
 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*X+a^2  1 a*X a*X a^2*X+1  1  1 a*X a^2*X+a X+a^2 X+a  X
 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  X  X a*X  0  0 a*X  X a^2*X  0  X a^2*X a*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+672x^225+348x^226+456x^227+183x^228+1716x^229+612x^230+552x^231+198x^232+1800x^233+516x^234+708x^235+258x^236+1332x^237+576x^238+444x^239+105x^240+1536x^241+384x^242+396x^243+156x^244+1236x^245+384x^246+348x^247+72x^248+528x^249+144x^250+120x^251+24x^252+324x^253+108x^254+48x^255+24x^256+72x^257+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 1.97 seconds.