The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1  0  1  1  1  1  1 a^2*X a*X  1  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+a  1 a^2*X+1  0 a^2*X+a^2 a^2*X+a^2  a a^2  X  1 X+a a*X a*X a^2*X+1 X+1  1  1 a^2*X a*X+a  1  0  0
 0  0 a^2*X  0  0  0  X  X  X  X  X  X a^2*X a^2*X a*X a^2*X a^2*X  0 a^2*X a*X a^2*X  0 a^2*X a^2*X a*X a^2*X a*X a*X a*X  X a*X  0  X a^2*X  X a^2*X  0
 0  0  0  X  0  X a^2*X  0  X a^2*X  X  0 a*X a^2*X  0  0  X a*X  X  0 a^2*X  X a^2*X a*X  X a^2*X a*X a^2*X  X  X  0 a*X a^2*X  0  0 a*X  0
 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  X  X  0  0 a*X  0 a*X  X a*X a*X a^2*X a*X a^2*X  X  X a^2*X a^2*X a^2*X a^2*X a^2*X  0 a*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+60x^96+36x^97+24x^98+72x^99+153x^100+540x^101+240x^102+324x^103+168x^104+1140x^105+480x^106+624x^107+141x^108+2616x^109+912x^110+840x^111+144x^112+2988x^113+1032x^114+936x^115+84x^116+1740x^117+384x^118+276x^119+105x^120+156x^121+72x^124+60x^128+27x^132+3x^136+3x^140+3x^144

The gray image is a linear code over GF(4) with n=148, k=7 and d=96.
This code was found by Heurico 1.16 in 0.732 seconds.