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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+300x^159+783x^160+624x^161+912x^162+1668x^163+2037x^164+1332x^165+1776x^166+2400x^167+3075x^168+2256x^169+2532x^170+3576x^171+4050x^172+2376x^173+3132x^174+4080x^175+4788x^176+2664x^177+2892x^178+3588x^179+3960x^180+2028x^181+1884x^182+2160x^183+1920x^184+888x^185+624x^186+576x^187+342x^188+120x^189+72x^190+84x^191+27x^192+3x^196+3x^200+3x^208

The gray image is a linear code over GF(4) with n=232, k=8 and d=159.
This code was found by Heurico 1.16 in 15.9 seconds.