The generator matrix

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

generates a code of length 57 over F4[X]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+282x^152+708x^153+384x^154+876x^155+2214x^156+3396x^157+2052x^158+2880x^159+4860x^160+6936x^161+3684x^162+6144x^163+9006x^164+13668x^165+7032x^166+9780x^167+13347x^168+19008x^169+9888x^170+13500x^171+16767x^172+21264x^173+10320x^174+12600x^175+14613x^176+17832x^177+6756x^178+7128x^179+8481x^180+7764x^181+2568x^182+2196x^183+1818x^184+1500x^185+312x^186+192x^187+213x^188+84x^189+12x^190+36x^192+36x^196+3x^200+3x^212

The gray image is a linear code over GF(4) with n=228, k=9 and d=152.
This code was found by Heurico 1.16 in 211 seconds.