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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+126x^152+339x^156+405x^160+465x^164+192x^165+366x^168+1728x^169+414x^172+5184x^173+441x^176+5184x^177+348x^180+324x^184+348x^188+216x^192+171x^196+96x^200+24x^204+9x^208+3x^220

The gray image is a linear code over GF(4) with n=232, k=7 and d=152.
This code was found by Heurico 1.16 in 2.54 seconds.