The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+480x^101+768x^102+408x^103+858x^104+2148x^105+2760x^106+1140x^107+1923x^108+3648x^109+4512x^110+2040x^111+2754x^112+5088x^113+5952x^114+2832x^115+3447x^116+6072x^117+6096x^118+2352x^119+2313x^120+3516x^121+2616x^122+444x^123+453x^124+552x^125+336x^126+15x^128+9x^132+3x^136

The gray image is a linear code over GF(4) with n=152, k=8 and d=101.
This code was found by Heurico 1.16 in 13.3 seconds.