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  1 a*X  1  1 a^2*X a^2*X
 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 a^2  1 a^2*X+a a^2*X+a^2  1  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*X+a X+a^2 X+a^2  X a^2*X X+a^2
 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*X+a^2  X  X  X a*X 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+420x^180+1332x^181+444x^182+288x^183+1497x^184+3732x^185+1164x^186+396x^187+2940x^188+5400x^189+1692x^190+480x^191+3837x^192+6252x^193+1608x^194+624x^195+3888x^196+6324x^197+1992x^198+660x^199+3552x^200+6216x^201+1440x^202+432x^203+2520x^204+3228x^205+720x^206+156x^207+726x^208+1224x^209+156x^210+36x^211+72x^212+84x^213+3x^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 22.5 seconds.