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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+318x^148+60x^149+192x^151+855x^152+384x^153+384x^155+1608x^156+504x^157+576x^159+2319x^160+672x^161+960x^163+2247x^164+780x^165+768x^167+1992x^168+576x^169+192x^171+678x^172+96x^173+96x^176+60x^180+24x^184+21x^188+6x^192+9x^196+3x^200+3x^204

The gray image is a linear code over GF(4) with n=216, k=7 and d=148.
This code was found by Heurico 1.16 in 1.17 seconds.