The generator matrix

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

generates a code of length 59 over F4[X]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+360x^162+660x^163+618x^164+600x^165+2112x^166+1920x^167+1308x^168+1284x^169+3516x^170+3612x^171+1989x^172+1764x^173+3972x^174+4104x^175+2451x^176+1896x^177+4764x^178+5088x^179+2463x^180+1704x^181+4692x^182+3696x^183+2034x^184+1500x^185+2640x^186+2028x^187+747x^188+444x^189+888x^190+360x^191+150x^192+24x^193+96x^194+36x^195+15x^196

The gray image is a linear code over GF(4) with n=236, k=8 and d=162.
This code was found by Heurico 1.16 in 16.1 seconds.