The generator matrix

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

generates a code of length 37 over F4[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+162x^96+216x^97+84x^98+636x^99+1371x^100+948x^101+312x^102+2040x^103+3357x^104+2304x^105+528x^106+4008x^107+5307x^108+3576x^109+768x^110+7008x^111+7158x^112+4776x^113+708x^114+5628x^115+6375x^116+2868x^117+552x^118+2184x^119+1710x^120+672x^121+120x^122+69x^124+51x^128+30x^132+9x^136

The gray image is a linear code over GF(4) with n=148, k=8 and d=96.
This code was found by Heurico 1.16 in 9.6 seconds.