The generator matrix

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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 185.

Homogenous weight enumerator: w(x)=1x^0+288x^185+468x^186+384x^187+1041x^188+1344x^189+1680x^190+1332x^191+2082x^192+2592x^193+2568x^194+1680x^195+2628x^196+3540x^197+3444x^198+1872x^199+3063x^200+4104x^201+3648x^202+2172x^203+3237x^204+3912x^205+3504x^206+1764x^207+2613x^208+2736x^209+2160x^210+1080x^211+1326x^212+1284x^213+780x^214+408x^215+345x^216+168x^217+180x^218+60x^219+48x^220

The gray image is a linear code over GF(4) with n=268, k=8 and d=185.
This code was found by Heurico 1.16 in 18.8 seconds.