The generator matrix

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

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+345x^188+384x^189+552x^190+840x^191+1572x^192+1476x^193+1644x^194+1752x^195+2601x^196+2388x^197+2076x^198+3048x^199+3645x^200+2484x^201+2520x^202+2856x^203+4230x^204+2904x^205+2772x^206+2748x^207+4140x^208+3036x^209+2328x^210+2532x^211+2784x^212+1800x^213+1296x^214+1260x^215+1425x^216+816x^217+564x^218+300x^219+237x^220+60x^221+72x^222+24x^223+9x^224+12x^225+3x^228

The gray image is a linear code over GF(4) with n=272, k=8 and d=188.
This code was found by Heurico 1.16 in 19.2 seconds.