The generator matrix

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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 181.

Homogenous weight enumerator: w(x)=1x^0+372x^181+732x^182+552x^183+672x^184+2052x^185+3360x^186+1932x^187+2067x^188+4944x^189+7320x^190+3756x^191+3885x^192+8340x^193+11892x^194+5964x^195+6885x^196+13848x^197+18384x^198+8364x^199+8226x^200+17352x^201+21192x^202+9120x^203+9189x^204+16728x^205+19500x^206+7620x^207+6483x^208+11028x^209+11220x^210+4284x^211+2874x^212+4260x^213+4140x^214+1308x^215+519x^216+876x^217+528x^218+108x^219+84x^220+72x^221+36x^222+33x^224+6x^228+15x^232+12x^236+6x^240+3x^244

The gray image is a linear code over GF(4) with n=268, k=9 and d=181.
This code was found by Heurico 1.16 in 277 seconds.