The generator matrix

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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+12x^265+144x^266+60x^267+258x^268+216x^269+516x^270+324x^271+663x^272+408x^273+996x^274+468x^275+585x^276+480x^277+1056x^278+516x^279+582x^280+588x^281+924x^282+528x^283+774x^284+504x^285+948x^286+636x^287+534x^288+480x^289+732x^290+372x^291+369x^292+240x^293+600x^294+156x^295+195x^296+144x^297+180x^298+12x^299+27x^300+48x^302+27x^304+21x^308+15x^312+12x^316+6x^320+12x^324+3x^328+3x^332+3x^336+3x^340+3x^344

The gray image is a linear code over GF(4) with n=376, k=7 and d=265.
This code was found by Heurico 1.16 in 28.4 seconds.