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

generates a code of length 68 over F4[X]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+462x^184+504x^185+300x^186+1104x^187+2925x^188+2400x^189+1380x^190+3096x^191+7179x^192+4128x^193+2808x^194+6156x^195+11994x^196+7512x^197+4356x^198+9240x^199+17985x^200+11604x^201+5484x^202+13344x^203+22602x^204+12864x^205+7032x^206+13212x^207+22311x^208+12288x^209+5616x^210+9660x^211+15642x^212+7416x^213+2676x^214+4512x^215+6138x^216+2268x^217+960x^218+1032x^219+1140x^220+432x^221+108x^222+84x^223+93x^224+24x^225+21x^228+24x^232+9x^236+12x^240+3x^244+3x^248

The gray image is a linear code over GF(4) with n=272, k=9 and d=184.
This code was found by Heurico 1.16 in 278 seconds.