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

generates a code of length 97 over F4[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+165x^272+372x^273+72x^274+696x^275+1233x^276+1500x^277+204x^278+1464x^279+2616x^280+2268x^281+384x^282+1944x^283+3486x^284+3192x^285+564x^286+2172x^287+4293x^288+3492x^289+456x^290+2760x^291+4308x^292+3372x^293+492x^294+2292x^295+4017x^296+3288x^297+480x^298+2004x^299+3024x^300+2232x^301+204x^302+1332x^303+1767x^304+1248x^305+144x^306+552x^307+519x^308+432x^309+72x^310+132x^311+90x^312+84x^313+12x^315+30x^316+24x^317+12x^320+15x^324+9x^328+6x^332+3x^340+3x^344+3x^360

The gray image is a linear code over GF(4) with n=388, k=8 and d=272.
This code was found by Heurico 1.16 in 30.4 seconds.