The generator matrix

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

generates a code of length 74 over F4[X]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+138x^208+189x^212+48x^213+180x^216+432x^217+117x^220+1296x^221+87x^224+1296x^225+90x^228+51x^232+39x^236+36x^240+15x^244+36x^248+18x^252+6x^256+6x^260+9x^264+3x^268+3x^284

The gray image is a linear code over GF(4) with n=296, k=6 and d=208.
This code was found by Heurico 1.16 in 0.27 seconds.