The generator matrix

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

generates a code of length 74 over F4[X]/(X^2) who´s minimum homogenous weight is 207.

Homogenous weight enumerator: w(x)=1x^0+1500x^207+921x^208+4536x^211+1818x^212+7104x^215+2508x^216+9144x^219+2880x^220+9372x^223+2955x^224+8292x^227+2676x^228+5976x^231+1812x^232+2544x^235+672x^236+624x^239+123x^240+60x^243+18x^244

The gray image is a linear code over GF(4) with n=296, k=8 and d=207.
This code was found by Heurico 1.16 in 888 seconds.