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

generates a code of length 48 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+210x^136+192x^137+240x^138+144x^139+576x^140+432x^141+204x^142+108x^143+432x^144+192x^145+132x^146+36x^147+267x^148+168x^149+108x^150+84x^151+162x^152+144x^153+60x^154+12x^155+138x^156+24x^157+24x^158+3x^160+3x^164

The gray image is a linear code over GF(4) with n=192, k=6 and d=136.
This code was found by Heurico 1.16 in 0.047 seconds.