The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  1  0  1  1  2  1  X  1  1  1  2  0  1  X  0  1  1  1  2 X+2  1  1
 0  1  0  X  1 X+3  1 X+2  0  2  1  1  1  1  X  1 X+1  0  1 X+3  X X+1  2  0  1  0  3  1  1  X  2  X  1  1 X+3  X
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  X  X X+1  X X+1 X+1 X+1  X  1  1  0  1  0  3  1  0 X+3  2  X X+3  1  3  0  X  1
 0  0  0  2  0  0  0  0  2  2  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  2  2  2  0  2  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  0  2  0  2  2  2  2  2  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  2  2  2  0  0  2  2  0  0  2  2  0  0
 0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  0  2  2  2  2  0  0  2  2  2  2  0  2  0  0  0  0

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+55x^28+142x^29+276x^30+688x^31+751x^32+1510x^33+1571x^34+2226x^35+1916x^36+2338x^37+1498x^38+1554x^39+794x^40+594x^41+216x^42+134x^43+61x^44+24x^45+18x^46+6x^47+6x^48+5x^50

The gray image is a code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 5.1 seconds.