The generator matrix

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

generates a code of length 74 over F4[X]/(X^2) who´s minimum homogenous weight is 211.

Homogenous weight enumerator: w(x)=1x^0+1260x^211+447x^212+2400x^215+1065x^216+2280x^219+675x^220+2208x^223+678x^224+1848x^227+612x^228+1224x^231+408x^232+816x^235+135x^236+216x^239+63x^240+36x^243+3x^244+9x^248

The gray image is a linear code over GF(4) with n=296, k=7 and d=211.
This code was found by Heurico 1.16 in 69 seconds.