The generator matrix

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

generates a code of length 74 over F4[X]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+213x^204+228x^205+72x^206+456x^207+1851x^208+684x^209+468x^210+1152x^211+3570x^212+1344x^213+720x^214+1524x^215+5079x^216+1920x^217+1212x^218+2040x^219+6345x^220+2448x^221+1152x^222+2484x^223+6888x^224+2424x^225+1164x^226+2640x^227+5688x^228+1968x^229+912x^230+1404x^231+3414x^232+864x^233+420x^234+504x^235+1515x^236+348x^237+24x^238+84x^239+159x^240+60x^241+21x^244+33x^248+12x^252+9x^256+9x^260+6x^264+3x^268

The gray image is a linear code over GF(4) with n=296, k=8 and d=204.
This code was found by Heurico 1.16 in 22.3 seconds.