The generator matrix

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

generates a code of length 65 over F4[X]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+216x^178+300x^179+426x^180+420x^181+1392x^182+924x^183+1404x^184+1128x^185+2700x^186+1404x^187+2400x^188+1932x^189+3828x^190+1992x^191+2856x^192+2400x^193+5052x^194+2568x^195+3486x^196+2652x^197+5016x^198+2424x^199+3288x^200+2472x^201+4116x^202+1836x^203+1755x^204+1140x^205+1908x^206+696x^207+579x^208+144x^209+300x^210+132x^211+105x^212+48x^214+12x^215+18x^216+24x^220+18x^224+9x^228+12x^232+3x^236

The gray image is a linear code over GF(4) with n=260, k=8 and d=178.
This code was found by Heurico 1.16 in 23.8 seconds.