The generator matrix

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

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+138x^156+12x^157+204x^159+912x^160+252x^161+384x^163+1248x^164+552x^165+456x^167+2094x^168+600x^169+720x^171+2466x^172+828x^173+876x^175+2073x^176+684x^177+336x^179+981x^180+144x^181+96x^183+195x^184+42x^188+48x^192+12x^196+9x^200+6x^204+6x^208+3x^212+6x^216

The gray image is a linear code over GF(4) with n=228, k=7 and d=156.
This code was found by Heurico 1.16 in 1.25 seconds.