The generator matrix

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

generates a code of length 68 over F4[X]/(X^2) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+75x^188+156x^190+216x^191+606x^192+252x^194+804x^195+1023x^196+336x^198+936x^199+1167x^200+696x^202+1296x^203+1317x^204+780x^206+1464x^207+1506x^208+540x^210+1044x^211+1035x^212+264x^214+360x^215+267x^216+48x^218+24x^219+57x^220+36x^224+21x^228+27x^232+15x^236+9x^244+3x^248+3x^256

The gray image is a linear code over GF(4) with n=272, k=7 and d=188.
This code was found by Heurico 1.16 in 1.52 seconds.