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

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+273x^192+84x^194+288x^195+831x^196+348x^198+900x^199+972x^200+492x^202+1092x^203+1146x^204+648x^206+1320x^207+1383x^208+924x^210+1512x^211+1146x^212+444x^214+852x^215+930x^216+132x^218+180x^219+279x^220+102x^224+36x^228+24x^232+15x^236+21x^240+3x^244+6x^248

The gray image is a linear code over GF(4) with n=276, k=7 and d=192.
This code was found by Heurico 1.16 in 1.59 seconds.