The generator matrix

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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 189.

Homogenous weight enumerator: w(x)=1x^0+372x^189+624x^190+276x^191+39x^192+1056x^193+1320x^194+456x^195+57x^196+1500x^197+1428x^198+576x^199+57x^200+1308x^201+1248x^202+372x^203+57x^204+1176x^205+1032x^206+276x^207+9x^208+1044x^209+744x^210+192x^211+9x^212+360x^213+372x^214+120x^215+3x^216+96x^217+144x^218+36x^219+15x^220+3x^224+6x^228

The gray image is a linear code over GF(4) with n=268, k=7 and d=189.
This code was found by Heurico 1.16 in 0.969 seconds.