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

generates a code of length 57 over F4[X]/(X^2) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+180x^155+450x^156+504x^157+348x^158+1344x^159+1629x^160+1512x^161+1128x^162+2640x^163+2589x^164+2172x^165+1236x^166+3792x^167+3735x^168+3084x^169+2136x^170+4572x^171+4197x^172+3552x^173+2436x^174+5088x^175+3993x^176+3024x^177+1464x^178+3000x^179+2157x^180+1260x^181+396x^182+816x^183+558x^184+252x^185+72x^186+72x^187+54x^188+30x^192+42x^196+3x^200+12x^204+3x^208+3x^220

The gray image is a linear code over GF(4) with n=228, k=8 and d=155.
This code was found by Heurico 1.16 in 16.3 seconds.