The generator matrix

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

generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+171x^176+330x^180+456x^184+852x^188+2130x^192+4053x^196+4593x^200+2565x^204+402x^208+243x^212+213x^216+153x^220+126x^224+42x^228+30x^232+18x^236+6x^240

The gray image is a linear code over GF(4) with n=264, k=7 and d=176.
This code was found by Heurico 1.16 in 2.98 seconds.