The generator matrix

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

generates a code of length 57 over F4[X]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+78x^148+285x^152+363x^156+48x^159+456x^160+576x^163+432x^164+2592x^167+405x^168+5184x^171+417x^172+3888x^175+390x^176+360x^180+345x^184+234x^188+159x^192+111x^196+33x^200+18x^204+6x^208+3x^212

The gray image is a linear code over GF(4) with n=228, k=7 and d=148.
This code was found by Heurico 1.16 in 2.47 seconds.