The generator matrix

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

generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 183.

Homogenous weight enumerator: w(x)=1x^0+540x^183+912x^184+816x^185+708x^186+1944x^187+2004x^188+1920x^189+1356x^190+2976x^191+3042x^192+2652x^193+1596x^194+3876x^195+3672x^196+3048x^197+1944x^198+4440x^199+3675x^200+2964x^201+1632x^202+4128x^203+3354x^204+2400x^205+1284x^206+2592x^207+2049x^208+1236x^209+564x^210+900x^211+708x^212+312x^213+120x^214+108x^215+33x^216+12x^217+12x^218+6x^220

The gray image is a linear code over GF(4) with n=264, k=8 and d=183.
This code was found by Heurico 1.16 in 555 seconds.