The generator matrix

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

generates a code of length 57 over F4[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+321x^156+564x^157+504x^158+960x^159+2085x^160+1572x^161+1584x^162+1728x^163+2958x^164+2352x^165+2064x^166+2592x^167+4185x^168+3564x^169+2520x^170+3180x^171+5205x^172+3948x^173+2544x^174+2664x^175+4389x^176+3204x^177+2088x^178+1968x^179+2622x^180+1488x^181+840x^182+600x^183+651x^184+204x^185+144x^186+132x^187+96x^188+9x^192+6x^196

The gray image is a linear code over GF(4) with n=228, k=8 and d=156.
This code was found by Heurico 1.16 in 16.1 seconds.