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

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+456x^189+564x^190+264x^191+42x^192+1032x^193+1320x^194+456x^195+54x^196+1404x^197+1500x^198+516x^199+63x^200+1380x^201+1260x^202+420x^203+42x^204+1176x^205+1128x^206+324x^207+18x^208+840x^209+588x^210+228x^211+12x^212+516x^213+408x^214+96x^215+6x^216+108x^217+144x^218+9x^220+3x^224+3x^232+3x^236

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 1.28 seconds.