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  1  1  1  1  1 a*X  1  1  1  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^2  1 X+a^2 a*X a*X+a a*X X+a^2 X+a a*X+a^2 a*X X+1  0  0 X+a a*X+1 a*X+1 a^2*X+1 a^2*X+1
 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*X+a^2 a^2 a*X+a a*X a*X+1 a^2*X+1  X X+a^2 a*X+1 a^2 a^2*X+a^2  1 a^2*X+a^2 a^2*X+1 a^2*X+a^2 X+a a*X+a a^2*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 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  0  0 a*X a*X a^2*X  0  0 a*X  X a^2*X a^2*X  0 a*X a*X a*X  0 a^2*X a*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+1200x^211+510x^212+2268x^215+927x^216+2652x^219+765x^220+2184x^223+675x^224+1824x^227+549x^228+984x^231+447x^232+792x^235+189x^236+372x^239+30x^240+12x^243+3x^260

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 22.8 seconds.