The generator matrix

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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 193.

Homogenous weight enumerator: w(x)=1x^0+144x^193+168x^194+792x^195+90x^196+192x^197+288x^198+792x^199+78x^200+144x^201+108x^202+144x^203+30x^204+144x^205+12x^206+24x^208+96x^209+156x^210+504x^211+18x^212+48x^213+36x^214+72x^215+6x^216+6x^220+3x^224

The gray image is a linear code over GF(4) with n=268, k=6 and d=193.
This code was found by Heurico 1.16 in 92 seconds.