The generator matrix

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

generates a code of length 68 over F4[X]/(X^2) who´s minimum homogenous weight is 197.

Homogenous weight enumerator: w(x)=1x^0+468x^197+588x^198+240x^199+21x^200+492x^201+444x^202+132x^203+24x^204+276x^205+288x^206+96x^207+168x^209+192x^210+60x^211+6x^212+204x^213+132x^214+24x^215+6x^216+60x^217+36x^218+24x^219+60x^221+48x^222+3x^228+3x^236

The gray image is a linear code over GF(4) with n=272, k=6 and d=197.
This code was found by Heurico 1.16 in 85.8 seconds.