The generator matrix

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

generates a code of length 73 over F4[X]/(X^2) who´s minimum homogenous weight is 203.

Homogenous weight enumerator: w(x)=1x^0+288x^203+540x^204+720x^205+852x^206+1236x^207+2148x^208+1872x^209+1776x^210+2052x^211+3207x^212+2352x^213+2376x^214+2568x^215+3516x^216+2580x^217+2592x^218+2976x^219+3768x^220+2796x^221+2580x^222+2772x^223+3822x^224+2808x^225+1992x^226+1992x^227+2682x^228+1500x^229+1272x^230+1140x^231+1098x^232+648x^233+360x^234+324x^235+192x^236+72x^237+24x^238+12x^239+15x^240+12x^241+3x^244

The gray image is a linear code over GF(4) with n=292, k=8 and d=203.
This code was found by Heurico 1.16 in 22.8 seconds.