The generator matrix

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

generates a code of length 48 over F4[X]/(X^2) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+588x^137+144x^138+276x^139+255x^140+588x^141+60x^142+204x^143+210x^144+432x^145+72x^146+168x^147+84x^148+276x^149+60x^150+60x^151+66x^152+348x^153+48x^154+60x^155+21x^156+72x^157+3x^160

The gray image is a linear code over GF(4) with n=192, k=6 and d=137.
This code was found by Heurico 1.16 in 55.5 seconds.