The generator matrix

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

generates a code of length 69 over F4[X]/(X^2) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+1341x^192+1188x^194+4128x^196+2316x^198+6858x^200+3024x^202+8724x^204+3684x^206+9126x^208+3180x^210+8328x^212+2988x^214+6078x^216+1584x^218+2124x^220+420x^222+372x^224+48x^226+24x^228

The gray image is a linear code over GF(4) with n=276, k=8 and d=192.
This code was found by Heurico 1.16 in 119 seconds.