The generator matrix

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

generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+324x^184+252x^185+192x^186+753x^188+672x^189+408x^190+1194x^192+1068x^193+456x^194+1179x^196+1320x^197+720x^198+1668x^200+1380x^201+816x^202+1260x^204+1056x^205+408x^206+441x^208+372x^209+72x^210+210x^212+24x^213+42x^216+27x^220+21x^224+15x^228+18x^232+12x^236+3x^240

The gray image is a linear code over GF(4) with n=264, k=7 and d=184.
This code was found by Heurico 1.16 in 1.64 seconds.