The generator matrix

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

generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+456x^232+444x^233+744x^234+420x^235+1443x^236+1548x^237+1740x^238+696x^239+2850x^240+2352x^241+2988x^242+828x^243+3684x^244+3144x^245+2928x^246+984x^247+3780x^248+3300x^249+3372x^250+1320x^251+3882x^252+3252x^253+2868x^254+936x^255+3411x^256+2712x^257+2100x^258+540x^259+2046x^260+1200x^261+1368x^262+360x^263+732x^264+408x^265+300x^266+60x^267+147x^268+72x^269+24x^270+33x^272+18x^276+21x^280+12x^284+9x^288+3x^296

The gray image is a linear code over GF(4) with n=332, k=8 and d=232.
This code was found by Heurico 1.16 in 40.9 seconds.