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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+144x^188+12x^189+207x^192+144x^193+201x^196+648x^197+135x^200+1296x^201+78x^204+972x^205+54x^208+24x^212+57x^216+36x^220+24x^224+27x^228+12x^232+9x^236+6x^244+6x^248+3x^252

The gray image is a linear code over GF(4) with n=268, k=6 and d=188.
This code was found by Heurico 1.16 in 49.1 seconds.