The generator matrix

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

generates a code of length 72 over F4[X]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+510x^196+468x^197+744x^198+960x^199+3357x^200+2256x^201+2460x^202+2388x^203+7239x^204+4284x^205+4896x^206+4440x^207+11970x^208+6744x^209+7440x^210+6528x^211+17799x^212+9792x^213+10596x^214+8652x^215+22647x^216+11352x^217+12252x^218+8604x^219+21063x^220+10572x^221+9720x^222+7008x^223+15657x^224+6888x^225+5448x^226+3288x^227+6444x^228+2436x^229+1500x^230+1020x^231+1683x^232+504x^233+240x^234+120x^235+108x^236+18x^240+12x^244+21x^248+6x^252+6x^256+3x^260

The gray image is a linear code over GF(4) with n=288, k=9 and d=196.
This code was found by Heurico 1.16 in 306 seconds.