The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+216x^97+312x^98+816x^99+1278x^100+1572x^101+2712x^102+2604x^103+4191x^104+4752x^105+6780x^106+5868x^107+9576x^108+11400x^109+14088x^110+11964x^111+15345x^112+19224x^113+21648x^114+18024x^115+19095x^116+19092x^117+20040x^118+11556x^119+12939x^120+9696x^121+7452x^122+3996x^123+2982x^124+1632x^125+696x^126+468x^127+57x^128+27x^132+24x^136+12x^140+3x^144+6x^148

The gray image is a linear code over GF(4) with n=152, k=9 and d=97.
This code was found by Heurico 1.16 in 122 seconds.