The generator matrix

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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+51x^184+252x^187+297x^188+1320x^191+588x^192+1776x^195+543x^196+2460x^199+855x^200+2892x^203+660x^204+2448x^207+627x^208+1032x^211+267x^212+108x^215+75x^216+48x^220+12x^224+45x^228+9x^232+9x^236+6x^240+3x^244

The gray image is a linear code over GF(4) with n=268, k=7 and d=184.
This code was found by Heurico 1.16 in 1.5 seconds.