The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+627x^104+300x^105+684x^107+1893x^108+636x^109+708x^111+2673x^112+756x^113+636x^115+2517x^116+852x^117+780x^119+1857x^120+432x^121+264x^123+642x^124+96x^125+18x^128+9x^132+3x^140

The gray image is a linear code over GF(4) with n=152, k=7 and d=104.
This code was found by Heurico 1.16 in 0.706 seconds.