The generator matrix

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

generates a code of length 75 over F4[X]/(X^2) who´s minimum homogenous weight is 213.

Homogenous weight enumerator: w(x)=1x^0+552x^213+468x^214+300x^215+276x^216+1164x^217+1020x^218+408x^219+453x^220+1416x^221+1080x^222+564x^223+315x^224+1260x^225+1092x^226+396x^227+342x^228+912x^229+840x^230+276x^231+147x^232+732x^233+432x^234+240x^235+180x^236+528x^237+324x^238+108x^239+66x^240+300x^241+96x^242+12x^243+6x^244+48x^245+24x^246+3x^248+3x^252

The gray image is a linear code over GF(4) with n=300, k=7 and d=213.
This code was found by Heurico 1.16 in 1.4 seconds.