The generator matrix

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

generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 250.

Homogenous weight enumerator: w(x)=1x^0+384x^250+744x^251+384x^252+588x^253+1764x^254+1836x^255+1344x^256+1152x^257+2964x^258+3036x^259+1623x^260+1272x^261+3660x^262+3432x^263+2196x^264+1596x^265+3888x^266+3684x^267+2103x^268+1536x^269+3696x^270+3360x^271+1650x^272+1512x^273+3240x^274+2724x^275+1365x^276+1008x^277+2160x^278+1704x^279+747x^280+420x^281+900x^282+852x^283+309x^284+108x^285+384x^286+132x^287+51x^288+24x^289+3x^296

The gray image is a linear code over GF(4) with n=356, k=8 and d=250.
This code was found by Heurico 1.16 in 28.8 seconds.