The generator matrix

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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+156x^157+276x^158+300x^159+375x^160+1032x^161+1428x^162+636x^163+720x^164+3168x^165+2244x^166+1080x^167+1107x^168+4704x^169+3684x^170+1800x^171+1221x^172+5460x^173+5184x^174+2280x^175+1605x^176+6696x^177+4764x^178+1788x^179+1308x^180+4536x^181+3060x^182+1032x^183+555x^184+1680x^185+780x^186+288x^187+156x^188+216x^189+84x^190+12x^191+39x^192+33x^196+18x^200+12x^204+12x^208+3x^212+3x^220

The gray image is a linear code over GF(4) with n=232, k=8 and d=157.
This code was found by Heurico 1.16 in 25.7 seconds.