The generator matrix

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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+564x^163+480x^164+696x^165+1404x^167+768x^168+1020x^169+1464x^171+867x^172+1008x^173+1776x^175+876x^176+816x^177+1272x^179+519x^180+624x^181+864x^183+468x^184+276x^185+300x^187+93x^188+168x^189+36x^191+15x^192+9x^196

The gray image is a linear code over GF(4) with n=232, k=7 and d=163.
This code was found by Heurico 1.16 in 2.05 seconds.