The generator matrix

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

generates a code of length 69 over F4[X]/(X^2) who´s minimum homogenous weight is 187.

Homogenous weight enumerator: w(x)=1x^0+264x^187+738x^188+792x^189+1104x^190+1776x^191+3195x^192+2628x^193+2712x^194+4332x^195+6618x^196+4368x^197+4476x^198+7380x^199+11577x^200+7920x^201+7260x^202+11532x^203+16743x^204+10200x^205+10344x^206+14400x^207+18480x^208+12504x^209+10932x^210+13668x^211+17730x^212+9792x^213+7884x^214+9540x^215+10251x^216+5328x^217+3492x^218+3852x^219+3909x^220+1536x^221+864x^222+792x^223+744x^224+228x^225+84x^226+48x^227+63x^228+12x^232+21x^236+6x^240+15x^244+6x^248+3x^252

The gray image is a linear code over GF(4) with n=276, k=9 and d=187.
This code was found by Heurico 1.16 in 283 seconds.