The generator matrix

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

generates a code of length 65 over F4[X]/(X^2) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+588x^180+492x^181+1044x^182+504x^183+2073x^184+1980x^185+1980x^186+1176x^187+3450x^188+2832x^189+2808x^190+1512x^191+4668x^192+3192x^193+3216x^194+1308x^195+4515x^196+3264x^197+3504x^198+1572x^199+4680x^200+2664x^201+2700x^202+1116x^203+2928x^204+1836x^205+1368x^206+396x^207+1017x^208+564x^209+264x^210+96x^211+135x^212+72x^213+12x^214+9x^216

The gray image is a linear code over GF(4) with n=260, k=8 and d=180.
This code was found by Heurico 1.16 in 19.5 seconds.