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

generates a code of length 64 over F4[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+99x^176+36x^177+156x^179+723x^180+252x^181+396x^183+1164x^184+432x^185+492x^187+1845x^188+540x^189+588x^191+2247x^192+708x^193+660x^195+2391x^196+756x^197+516x^199+1356x^200+264x^201+228x^203+276x^204+84x^205+36x^207+42x^208+12x^212+27x^216+24x^220+15x^224+6x^228+9x^232+3x^236

The gray image is a linear code over GF(4) with n=256, k=7 and d=176.
This code was found by Heurico 1.16 in 1.43 seconds.