The generator matrix

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

generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 182.

Homogenous weight enumerator: w(x)=1x^0+156x^182+408x^183+468x^184+1176x^185+1212x^186+1476x^187+1140x^188+2472x^189+2388x^190+2628x^191+1764x^192+3360x^193+3072x^194+2748x^195+2553x^196+3900x^197+3348x^198+3612x^199+2370x^200+3852x^201+2916x^202+3132x^203+1872x^204+3096x^205+2472x^206+2076x^207+1245x^208+1680x^209+1092x^210+708x^211+285x^212+420x^213+228x^214+108x^215+72x^216+12x^217+12x^218+6x^220

The gray image is a linear code over GF(4) with n=264, k=8 and d=182.
This code was found by Heurico 1.16 in 18.5 seconds.